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 of a circle.it was found that the area of the circle is greater than that of the rectangle by 104.5cmsq. find the length of the wire.

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Answer 1

Let the breadth be x

The length = 2x

Find the area of the rectangle:

Area = Length x Breadth

Area = 2x²

Find the perimeter of the rectangle:

Perimeter = 2(Length + breadth)

Perimeter = 2(2x + x)

Perimeter = 6x

Find the radius of the circle in term of x

Circumference = 2πr

2πr = 6x

r = 6x ÷ 2π

r = 3x/π

Find the area of the circle in term of x:

Area = πr²

Area = π(3x/π)² = 9x²/π

Solve x:

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

9x²/π -  2x² = 104.5

x² (9/π - 2) = 104.5

19/22 x² = 104.5

x²  = 104.5 ÷ 19/22

x² = 121

x = √121

x = 11 cm

Find the length of the wire:

Length = 6x = 6(11) = 66 cm

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