A wire is bent to form a square of side 11 cm. If this wire is reshaped to form a rectangle of length 16 cm, find the breadth of the rectangle and area of the rectangle.

Given:

A wire is bent to form a square of side 11 cm.

The wire is reshaped to form a rectangle of length 16 cm.

To do:

We have to find the breadth and area of the rectangle.

Solution:

 Side of square = 11 cm

Wire is reshaped from square to a rectangle.

So, Perimeter of square = Perimeter of rectangle

Perimeter of square = 4 $\times$ side

Perimeter of square = 4 $\times$ 11

Perimeter of square = 44 cm

So, Perimeter of rectangle = 44 cm

Length of rectangle = 16 cm

Perimeter of rectangle  =  2 (length $+$ breadth)

44 = 2 (16 $+$ breadth)

$\frac{44}{2} = 16 +$ breadth

$22 = 16 +$ breadth

$22 - 16 =$ breadth

breadth = 6 cm

The breadth of the rectangle is 6 cm.

Area of rectangle  =  length $\times$ breadth

Area of rectangle  = 16 $\times$ 6 cm² 

The area of the rectangle is 96 sq.cm.

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Updated on: 10-Oct-2022

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