Question

the perimeter of a rectangle and the perimeter of a square are equal if the side of a square is 8 cm and length of the rectangle is 12cm find the breadth of the rectangle​

Answer 1

Given :

• The perimeter of a rectangle and the perimeter of a square are equal.
• The side of a square is 8 cm.
• Length of the rectangle is 12cm.

To find :

• Breadth of the rectangle.

Solution :

• Side of square = 8 cm.

Then,

Perimeter of the square = 4 × side

→Perimeter of the square=(4 × 8) cm

→ Perimeter of the square = 32 cm.

Consider,

• Breadth of rectangle = x cm

Length of rectangle = 12 cm.

According to the question :-

• The perimeter of a rectangle and the perimeter of a square are equal.

$\implies\sf{2(12+x)=32}$

$\implies\sf{12+x=\dfrac{32}{2}}$

$\implies\sf{12+x=16}$

$\implies\sf{x=16-12}$

$\implies\sf{x=4}$

Therefore, breadth of the rectangle is 4 cm.

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Verification :-

• Length of rectangle = 12 cm
• Breadth of rectangle = 4 cm

According to the question,

perimeter of rectangle= perimeter of square

→ 2(12+4) = 32

→ 2 × 16 = 32

→ 32 = 32

Hence Verified !

Answer 2

✯✯ QUESTION ✯✯

The perimeter of a rectangle and the perimeter of a square are equal if the side of a square is 8 cm and length of the rectangle is 12cm find the breadth of the rectangle..

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✰✰ ANSWER ✰✰

$\longmapsto\tt{Side\:of\:Square=8cm}$

$\longmapsto\tt{\small{\boxed{\bold{\bold{\purple{\sf{Perimeter\:of\:Square=4\times{Side}}}}}}}}$

➥Putting Values : -

$\longmapsto\tt{4\times{8}}$

$\longmapsto\tt{Perimeter\:of\:Square=32cm}$

➙Now ,

$\longmapsto\tt{Length\:of\:Rectangle=12cm}$

$\longmapsto\tt{Let\:Breadth\:be=x\:cm}$

➜As Given that Perimeter of Rectangle and Perimeter of Square are equal..So,

$\longmapsto\tt{\small{\boxed{\bold{\bold{\orange{\sf{Perimeter\:of\:Rectangle=2(l+b)}}}}}}}$

➥Putting Values : -

$\longmapsto\tt{32=2(12+x)}$

$\longmapsto\tt{\cancel\dfrac{32}{2}=12+x}$

$\longmapsto\tt{16=12+x}$

$\longmapsto\tt{16-12=x}$

$\blue\longmapsto\:\large\underline{\boxed{\bf\green{x}\red{=}\pink{4}}}$

☛Breadth of Rectangle is 4cm...

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★Area of Rectangle = (length × breadth )

★Area of Square = ( Side × Side )