Question

The perimeter of a rectangle is same as the perimeter of a square of side 12 cm. If the length of the rectangle is 13 cm, find its breadth.​

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Answer 1

Answer:

Step-by-step explanation:

Given,

• Perimeter of a rectangle = Perimeter of a square.
• Side of square = 12 cm
• Length of the rectangle = 13 cm

To Find

• Breadth of the rectangle

Formula to be used,

• Perimeter of square = 4 × side
• Perimeter of rectangle = 2 × (Length + Breadth)

Solution,

We know that perimeter of a rectangle is equal to perimeter of a square.

⇒ Perimeter of a rectangle = Perimeter of a square.

⇒ 2 × (13 + Breadth) = 4 × 12

⇒ 13 + Breadth = 48/2

⇒ 13 + Breadth = 24

⇒ Breadth = 24 - 13

⇒ Breadth = 11 cm.

Hence, the breadth of the rectangle is 11 cm.

Answer 2

Answer:

Given :-

• The perimeter of a rectangle is same as the perimeter of a square of side 12 cm.
• The length of the rectangle is 13 cm.

To Find :-

• What is the breadth.

Formula Used :-

$\clubsuit$ Perimeter of a rectangle Formula :

$\small\mapsto \sf\boxed{\bold{\pink{Perimeter_{(Rectangle)} =\: 2(Length + Breadth)}}}$

$\clubsuit$ Perimeter of square Formula :

$\mapsto \sf\boxed{\bold{\pink{Perimeter_{(Square)} =\: 4a}}}$

where,

• a = Side of Square

Solution :-

Let,

$\mapsto \bf{Breadth\: of\: rectangle =\: x\: cm}$

Given :

• Side of square = 12 cm
• Length of the rectangle = 13 cm

According to the question by using the formula we get,

$\small\bigstar\: \: \sf\bold{\purple{Perimeter\: of\: Rectangle =\: Perimeter\: of\: Square}}$

$\longrightarrow \sf 2(Length + Breadth) =\: 4a$

$\longrightarrow \sf 2(13 + x) =\: 4(12)$

$\longrightarrow \sf 2(13 + x) =\: 4 \times 12$

$\longrightarrow \sf 26 + 2x =\: 48$

$\longrightarrow \sf 2x =\: 48 - 26$

$\longrightarrow \sf 2x =\: 22$

$\longrightarrow \sf x =\: \dfrac{\cancel{22}}{\cancel{2}}$

$\longrightarrow \sf x =\: \dfrac{11}{1}$

$\longrightarrow \sf\bold{\red{x =\: 11\: cm}}$

${\small{\bold{\underline{\therefore\: The\: breadth\: of\: rectangle\: is\: 11\: cm\: .}}}}$