Question

A wire is bent in the form of a rectangle having length twice the breadth. The same wire is bent in the form of a circle. It was found the area of the circle is greater than that of the rectangle by 104.5sqcm. Find the length of the wire

Answer 1

Answer:

66 cm

Step-by-step explanation:

Define x:

Let the breadth be x cm

The length = 2x cm

Find the perimeter of the rectangle:

Perimeter = 2(Length + Breadth)

Perimeter = 2(x + 2x) = 6x cm

Find the area of the rectangle:

Area = Length x Breadth

Area = (2x)(x) = 2x² cm²

Find the radius:

Circumference = 2πr

2πr = 6x

r = 6x ÷ 2π

r = 3x/π cm

Find the area of the circle:

Area = πr²

Area = π(3x/π)² = 63x²/22 m²

Solve x:

The area of the circle is greater than the rectangle by 104.5 cm²

63x²/22 - 2x² = 104.5

63x² - 44x² = 2299

19x² = 2299

x² = 121

x = √121

x = 11 cm

Find the length of the wire:

Length of the wire = 6x = 6(11) = 66 cm

Answer: 66 cm