Question

the area of a square is 64 cm 2 a rectangle has the same perimeter as the square if the length of the rectangle is 11 cm find its breadth

Answer 1

AnSwer -:

Breadth of Rectangle = 5 cm

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Step by Step Explanation -:


Area of square-:

“A = S x S”

Perimeter of a square-:

“P= 4 x S”

S = length of side of a square

P = Perimeter

A = Area

Perimeter of a Rectangle-:

“P= 2(l+b)”

P = Perimeter

L = length

B = breadth

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Given ,

Area of square = 64 cm^2 = side x side =

(Side)^2

Length of Rectangle = 11 cm

To find,

Breadth of Rectangle.

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Area of square = side x side= (side)^2

Side of a square = ??

Area of square = 64 cm^2

(Side)^2 = 64 cm^2

Side = ✓64

Side = 8 cm

Side of a square = 8cm


Perimeter of square 4 x s

Side of a square = 8 cm

4 x 8 =

= 32 cm

Perimeter of square = 32 cm

According to the question,

Perimeter of square = Perimeter of

Rectangle

Then ,

Formula of perimeter of rectangle-:

2(l+b)

Perimeter of rectangle-: 32 cm

Length of Rectangle-: 11 cm = l

Breadth of Rectangle-: ?? = b

2 (11 + b) = 32 cm

22 + 2b

2b = 32 - 22

2b = 10

B = 10/2

B= 5

Therefore,

Breadth of Rectangle = 5 cm

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Answer 2

Question:-

the area of a square is 64 cm² a rectangle has the same perimeter as the square if the length of the rectangle is 11 cm find its breadth

Answer:-

• The breadth of rectangle is 5 cm.

Solution:-

• Area of square = 64 cm²

$\purple{ \underline{ \underline{ \mathfrak{ \large{ \pink{area = {side}^{2} }}}}}}$

$\large{ \tt : \implies \: \: \: \: {side}^{2} = 64}$

$\large{ \tt : \implies \: \: \: \: side = \sqrt{64} }$

$\large{ \tt : \implies \: \: \: \: side = 8 \: cm}$

• The side of square is 8 cm

$\green{ \underline{ \underline{ \mathfrak{ \large{ \purple{perimeter = 4 \times side }}}}}}$

$\large{ \tt : \implies \: \: \: \: perimeter = 4 \times 8}$

$\large{ \tt : \implies \: \: \: \: perimeter =32 \: cm}$

• Perimeter of square = Perimeter of rectangle
• Length of Rectangle = 11 cm

$\orange{ \underline{ \underline{ \mathfrak{ \large{ \green{perimeter = 2(l + b)}}}}}}$

$\large{ \tt : \implies \: \: \: \: 2(11 + b) = 32}$

$\large{ \tt : \implies \: \: \: \: 11 + b = \frac{32}{2} }$

$\large{ \tt : \implies \: \: \: \: 11 + b = 16}$

$\large{ \tt : \implies \: \: \: \: b = 16 - 11}$

$\large{ \tt : \implies \: \: \: \: b = 5}$

• The breadth of rectangle is 5 cm.