Question

A wire when bent in the form of a square encloses an area of 16 cm². Find the area enclosed by it when the same wire is bent in the form of a rectangle whose sides are in the ratio of 1 : 3

Answer 1

Let the side of a square = x cm
Its area = 16cm2
⇒ x² = 16
⇒ x = 4cm
Clearly, the length of the wire
= Perimeter of a square
= 4 x 4 
= 16cm²
Let the breadth of a rectangle = b cm
⇒ Its length = 3b cm
Now, the perimeter of a rectangle = length of the wire
⇒ 2(3b + b) = 16
⇒ 4b = 8
⇒ b = 2cm = breadth
⇒ length
= 3b
= 3x2
= 6cm
∴ Area of a rectangle
= 6 x 2
= 12cm².