Question

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

Answer 1

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Define x:

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:

Length = 2x = 2(11) = 22 cm


Answer: The length is 22 cm.



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