Question

A circular wire of diameter 42 cm is folded in the shape of a rectangle whose sides are in the ratio 6 : 5. Find the area enclosed by the rectangle. (Take π = 22/7)
1. 500 cm²
2. 1080 cm²
3. 1020 cm²
4. 2020 cm²

Answer 1

Correct Answer - Option 2 : 1080 cm²

Given:

A circular wire of diameter 42 cm is folded in the shape of a rectangle whose sides are in the ratio 6 : 5.

Concept used:

Circumference of wire = 2πr

Perimeter of rectangle = 2(Length + Breadth)

Calculation:

Radius of circular wire = 42/2

Radius = 21 cm

Circumference of wire

2πr = 2 × 22/7 × 21

Circumference = 132 cm

Let the length of the rectangle be 6x and breadth be 5x.

Perimeter of rectangle = 2(6x + 5x)

Perimeter = 22x

22x = 132 cm

x = 6 cm

Length of rectangle = 6 × 6 = 36 cm

Breadth of rectangle = 5 × 6 = 30 cm

∴ Area = 30 × 36 = 1080 cm²