Mathematics High School

3. In a figure a small square is cutting out from the largesquare. The area of the remaining part is 91 cm². The sum of Sides equal to 52cm.
(a). If the side of large square is x and the side of smallest square is y then find the area of the remaining part?
(b). Find the sides of the smallest square?
(c). Find the areas of the two squares?

Answers

Answer 1

Step-by-step explanation:

[tex]\large\underline{\sf{Solution-}}[/tex]

Given that,

ABCD is a square of side x cm

EFGH is a square of side y cm

Further given that,

Sum of all sides = 52 cm

It means

Perimeter of square ABCD + Perimeter of square EFGH is 52 cm

We know,

[tex] \purple{\rm :\longmapsto\:\boxed{\tt{ Perimeter_{[square]} \: = \: 4 \times side \: }}}[/tex]

So, using this, we have

[tex]\rm :\longmapsto\:4x + 4y = 52[/tex]

[tex]\rm :\longmapsto\:4(x + y) = 52[/tex]

[tex]\rm\implies \:\boxed{\tt{ x + y = 13}} - - - - (1)[/tex]

Now, Further given that,

If square EFGH is cutting out from square ABCD, the area of remaining part is 91 square cm.

It means

[tex]\rm :\longmapsto\:Area_{[ABCD]} - Area_{[EFGH]} = 91[/tex]

We know,

[tex] \purple{\rm :\longmapsto\:\boxed{\tt{ Area_{[square]} = 4 \times side}}}[/tex]

So, using this, we get

[tex]\rm :\longmapsto\: {x}^{2} - {y}^{2} = 91[/tex]

can be further rewritten as using algebraic Identity,

[tex]\rm :\longmapsto\:(x + y)(x - y) = 91[/tex]

[tex]\rm :\longmapsto\:13(x - y) = 91[/tex]

[tex]\red{ \bigg\{ \sf \: \because \: using \: equation \: (1) \bigg\}}[/tex]

[tex]\rm\implies \:\boxed{\tt{ x - y = 7}} - - - - (2)[/tex]

On adding equation (1) and (2), we get

[tex]\rm :\longmapsto\:2x = 13 + 7[/tex]

[tex]\rm :\longmapsto\:2x = 20[/tex]

[tex]\rm\implies \:\boxed{ \: \bf \: \: x \: = \: 10 \:cm \: \: }[/tex]

On substituting the value of x in equation (1), we have

[tex]\rm :\longmapsto\:10 + y = 13[/tex]

[tex]\rm :\longmapsto\:y = 13 - 10[/tex]

[tex]\rm\implies \:\boxed{ \: \bf \: \: y \: = \: 3 \:cm \: \: }[/tex]

So,

[tex]\rm\implies \:\boxed{Side_{[square \: EFGH]} = y \: = 3 \: cm}[/tex]

and

[tex]\rm\implies \:\boxed{Side_{[square \: ABCD]} = x \: = 10 \: cm}[/tex]

Also,

[tex]\rm :\longmapsto\:\boxed{Area_{[square \: ABCD]} = {10}^{2} = 100 \: {cm}^{2} }[/tex]

[tex]\rm :\longmapsto\:\boxed{Area_{[squareEFGH] }\: = {3}^{2} = 9 \: {cm}^{2} }[/tex]

▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬

[tex]\begin{gathered}\begin{gathered}\boxed{\begin {array}{cc}\\ \dag\quad \Large\underline{\bf Formulas\:of\:Areas:-}\\ \\ \star\sf Square=(side)^2\\ \\ \star\sf Rectangle=Length\times Breadth \\\\ \star\sf Triangle=\dfrac{1}{2}\times Breadth\times Height \\\\ \star \sf Scalene\triangle=\sqrt {s (s-a)(s-b)(s-c)}\\ \\ \star \sf Rhombus =\dfrac {1}{2}\times d_1\times d_2 \\\\ \star\sf Rhombus =\:\dfrac {1}{2}d\sqrt {4a^2-d^2}\\ \\ \star\sf Parallelogram =Breadth\times Height\\\\ \star\sf Trapezium =\dfrac {1}{2}(a+b)\times Height \\ \\ \star\sf Equilateral\:Triangle=\dfrac {\sqrt{3}}{4}(side)^2\end {array}}\end{gathered}\end{gathered}[/tex]

Related Questions

Is 93.936 a rational number and can someone please explain how to know if it’s rational or not:)

Answers

Answer:

ofcs it's rational number

Step-by-step explanation:

this is bcs this number '93.936' do not contain recurring decimals

Select from the drop-down menus to correctly complete the statements about the expression a8+6b .
The expression a8+6b is a
A. Sum
B. Difference
. The term a8 is an added, but it is also a
A. quotient
B. Difference
. The term 6b is an added, but it is also a
A. Sum
B. Product

Answers

Expressions are used to show relationships between variables and constants

The expression [tex]\mathbf{\frac a8 + 6b}[/tex] is a sumThe term [tex]\mathbf{\frac a8}[/tex] is a quotientThe term 6b is a product.

The expression is given as:

[tex]\mathbf{\frac a8 + 6b}[/tex]

In the above expression, a/8 and 6b are added.

So, the expression [tex]\mathbf{\frac a8 + 6b}[/tex] is a sum

In [tex]\mathbf{\frac a8 }[/tex], a is divided by 8.

So, the term [tex]\mathbf{\frac a8}[/tex] is a quotient

Lastly, in 6b; 6 is multiplied by b.

So, the term 6b is a product.

Answers

Answer:

C) 7 10

Step-by-step explanation:

Answer:

g is your answer lolllllll

Solve the inequality 5z+8≥-7

Answers

Answer:

z≥−3

Step-by-step explanation:

1 Subtract 88 from both sides.

5z≥−7−8

2 Simplify -7-8−7−8 to -15−15.

5z≥−15

3 Divide both sides by 55.

z≥− 15/5

4 Simplify 15/5 to 3

z≥−3

[tex]\sf 9\times 4\times 16=?[/tex]

Answers

You can use a calculator. Its faster

576

9
X4
_
36
X16
_
576

How many solutions exist for the given equation?

0.75(x + 40) = 0.35(x + 20) + 0.35(x + 20)

Answers

Answer:

0.35

Step-by-step explanation:

Answer:

Just one

Step-by-step explanation:

Got it right on Edge 2022

The figures are similar. Find x ,

Answers

Answer:

8 cm

Step-by-step explanation:

Hello there! :)

We are given that these figures are similar.

It means that the sides are proportional. So

[tex]\frac{4}{6} =\frac{6}{x}[/tex]

Cross-multiply:

4x=36

Divide both sides by 4 to isolate x:

x=9 cm

Hope this helps!

~Just a gloomy teen who misses her best friend

[tex]GraceRosalia :-([/tex]

-5x-9 is greater than or equal to -4

Answers

Answer x is less than or equal to -1

Step-by-step explanation:

-5x-9 -4

-5x-9+9 -4+9

-5x 5

-5x/-5x 5/-5

x less than or equal to -1

Answer:

x [tex]\leq[/tex] -1

Step-by-step explanation:

(-5x - 9) [tex]\geq[/tex] -4

add 9 to both sides of the equation

-5x-9 [tex]\geq[/tex] -4

+9 +9

--------------------

the -9 and +9 cancel out

-5x [tex]\geq[/tex] 5

then, divide both sides by -5 to get x

-5x [tex]\geq[/tex] 5

------ -------

-5 -5

x [tex]\leq[/tex] -1

by the way, the sign changed from [tex]\geq[/tex] to [tex]\leq[/tex] because we divided by a negative number to get x.

Yuri descended 450 feet down a

mountain. Her elevation changed at a

steady rate over 3 hours. What was her

change in elevation per hour?

Answers

The change is 150 because you would divide 450/3

Which of these sets of angle measures could be the three angles in a triangle? a 40, 50, 60 b 50, 60, 70 c 60, 70, 80 d 70,80, 90

Answers

Answer:

It’s going to be B. 50+60+70=180 which is how many degrees are in a triangle.

It would be B because 50 + 60 + 70 is 180

Express 2700 as a product of prime numbers or find the prime factorization of 2700 leaving
your answer in index form or notation

Answers

2700
27 100

9 3 10 10

3 3 2 5 2 5

answer

2^2 x 3^3 x 5^2

hey i need help with question 3 i put 81.5% but i’ve been told it’s been wrong ?

Answers

68% because it’s between them

Marco is 3 inches tall. There are 2.54 centimeters in 1 inch. What is marcos height in centimeters?

Answers

Answer:

The answer is 190.5cm

Step-by-step explanation:

o solve this problem, we first need to convert marco's height to inches.

there are 12 inches in 1 foot.

multiply.

notice how ft cancel out because they are in opposite positions of the fraction.

add 72+3 to get marco's height in inches.

marco is 75inches.

with this information, we can solve for his height in cm.

write an equation.

solve.

marco is 190.5centimeters

hope this helps!

answer pls 10 - 3 + 5 ÷ 5 × 4

Answers

Answer: the answer is 11

Step-by-step explanation:

The sum of three numbers is 66. The second number is twice the first and six less than the third. find the numbers

Answers

Step-by-step explanation:

let the 1st number be x

and,

2nd number = 2x

3rd number = 2x + 6

their sum = 66

so, after inserting the values we got

→ x + 2x + 2x + 6 = 66

→ 5x + 6 = 66

→ 5x = 66 - 6 = 60

→ x = 60/5 = 12

→ x = 12

therefore,

1st number = x = 12

2nd number = 2x = 12 × 2 = 24

3rd number = 2x + 6 = 24 + 6 = 30

hope this answer helps you dear...take care and may u have a great day ahead!

NEED HELP ASAP!!
What is the measure of the angle

Answers

Hey! The measure of the angle is 127

The angle is a total of 180 degrees.

We have to find the total of what's in between the two blue lines.

To make it easier, we can take the total of what's not in the blue lines, 53, and subtract it from 180. This gives us 127. So in between both the blue lines, measures 127. Or, you can just count up from 53 to 180 individually.

Express as a trinomial.
(2x – 4)(x + 8)

Answers

Answer:

[tex](2x - 4)(x + 8) \\ 2x - 4(x + 8) \\ 2x - 4x + 32 \\ 2x + 32[/tex]

(2x - 4) (x + 8)
2x ( x + 8) -4(x + 8)
2x^2 + 16x - 4x - 32
2x^2 + 12x -32

solve 4 with exponent -4 without the exponent in other words

4 exponent -4 without exponent

Answers

Answer:

[tex] \frac{4}{1} \times \frac{4}{1} \times \frac{4}{1} \times \frac{4}{1} = \frac{256}{1} = - 256[/tex]

Step-by-step explanation:

I dont know if I'm right or not

but this is how I learned it

Solve.
Ms. Holmstrom set up a math problem to find out how much money her class spends for lunches at the cafeteria for over a 2-day period. On Monday, 14 students bought lunches in the cafeteria, and 16 students bought lunches on Thursday. If lunches cost $2.50 each, how much money has Ms. Holmstrom's class spent?

Answers

Answer:

They have spent $75

16+14 = 30

30 x 2.50 = 75

Step-by-step explanation:

Please help me asap!!!!!!!!

Answers

Answer:

7/4 and 3/8.

Step-by-step explanation:

You can get this by dividing all possible answers, and if the decimal stops you have a terminating decimal.

Marlena bought a car in 2010. As years passed, the value of the car decrease linearly, as shown in the table. What was the purchase price of the car in 2010, and how much does it decrease each year?

Answers

Answer:

Step-by-step explanation:

Difference between value as the years pass, ($22,050-$19,600 = $2,450)

To find purchase price: $22, 050 + $2,450 = $24,500

-22 x (- 58/209) what the answer?!?!

Answers

Answer:

-22 x ( -58/209) = 116/19

Step-by-step explanation:

Please help, I need answers!
Q1
Solve for x.
7(x + 5) - 6x = 55
50
20
60
90

Q2
c−1.5+6.8=0.6
Answer in a decimal please

Answers

Answer:

[tex]Q.1)\:x=20[/tex]

[tex]Q.2)c=-4.7[/tex]

Step-by-step explanation:

[tex]Q1)[/tex] [tex]7\left(x+5\right)-6x=55[/tex]

Use the distributive property to multiply 7 by x+5 :

[tex]x+35=55[/tex]

Subtract 35 from both sides:

[tex]x+35-35=55-35[/tex]

[tex]x=20[/tex]

___________________________

[tex]Q2)[/tex] [tex]c-1.5+6.8=0.6[/tex]

[tex]-1.5+6.8=5.3[/tex]

[tex]c+5.3=0.6[/tex]

Subtract 5.3 from both sides:

[tex]c+5.3-5.3=0.6-5.3[/tex]

[tex]c=-4.7[/tex]

____________________________

Please help me ASAP!!!!!!!!!!!

Answers

Smallest 2-digit number: 23

3-digit number closest to 300: 276

Hope it helps you! ✺ ✺ ✺ ✺ ✺ ✺ ✺

[tex]ANSWERED:\\GraceRosalia[/tex]

The smallest 2 digit is 23
Number closest to 300 is 376

*20 points* 7x + 24 = 2x - 6 How many solutions?

Answers

Answer:

x= -6

Step-by-step explanation:

so i'm thinking 1 solution.

(let me know if i'm wrong)

Answer:

infinitely many solutions.

Step-by-step explanation:

If solving an equation yields a statement that is true for a single value for the variable, like x = 3, then the equation has one solution. If solving an equation yields a statement that is always true, like 3 = 3, then the equation has

PLZZZZ HELP ME OUT GIVING OUT 100 POINTS PLZZZZZZZZZZZZZZZZZZZZZZZZZZZZ
The diagram shows two parallel lines cut by a transversal. One angle measure is shown.

Two lines that do not intersect. A third line intersects with both lines.

Find the values of a, b, c, d, e, f, and g. Do not include any labels or degree symbols.

a=
b=
c=
d=
e=
f=
g=

Answers

Answer:

See below

Step-by-step explanation:

a + 54° = 180° [Angles on a straight line]

a = 180 - 54

a = 126°

a + b = 180 [Angles on a straight line add up to 180 degrees]

126 + b = 180

b = 180 - 126

b = 54°

c° = a° [Vertically opposite angles are equal]

c° = 126°

d = 54° [Corresponding angles are equal]

e = a [Corresponding angles are equal]

e = 126°

f = b [Corresponding angles are equal]

f = 54°

g = c [Corresponding angles]

g = 126°

[tex]\rule[225]{225}{2}[/tex]

Hope this helped!

~AH1807

I’m so bad at this I need to get this done ASAP NOW

Answers

Answer:

Step-by-step explanation:

The correct answer is A. 9

Explanation:

you need to make a common denominator, so multiply the left side by -3. then change to multiplication and flip the right side to -9/2. you will then multiply to get -162/-18 which equals nine.

please mark brainliest :)

Please answer the math problem... I will mark you brainliest

Answers

Comment has been deleted

Someone pls help me I will make you as brain

Answers

Answer:

B: shift vertically up by 3

Step-by-step explanation:

I suggest using desmos graphing for future questions like these

Hope this helps :)

A local foundation organized a lunch party for all the kids in the community. They ordered a total of 500 burger meals. They ordered plain burgers at $1.75 each cheeseburgers at $2.50 each, and chicken burgers
at $3.20 each. They ordered mostly cheeseburgers, and 100 fewer chicken burgers than plain burgers. The total order came to $1.172.50.
Define the variables and write a system of equations to represent the
situation.

Answers

9514 1404 393

Answer:

x + y + z = 5002.50x +1.75y +3.20z = 1172.500x +y -z = 100

Step-by-step explanation:

Let x, y, z represent the numbers of cheeseburgers, plain burgers, and chicken burgers ordered for the party.

We have three relations given. Each can be used to write an equation.

x + y + z = 500 . . . . . . . . . a total of 500 meals were ordered

2.50x +1.75y +3.20z = 1172.50 . . . . . the total cost

0x +y -z = 100 . . . . . . . . . . 100 fewer chicken were ordered than plain

_____

Additional comment

We put the coefficient of x as 0 in the last equation to facilitate writing this system as an augmented matrix.

[tex]\left[\begin{array}{ccc|c}1&1&1&500\\2.50&1.75&3.20&1172.50\\0&1&-1&100\end{array}\right][/tex]

The solution is (x, y, z) = (300, 150, 50).

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