A wire is bent in the form of a rectangle having length twice the brea

1.	A wire is bent in the form of a rectangle having length twice the breadth. The samewire is bent in the form of a circle. It was found that the area of the circle is greaterthan that of the rectangle by 104.5 cm2. Find the length of the wire.
Answer» 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

A wire is bent in the form of a rectangle having length twice the breadth. The samewire is bent in the form of a circle. It was found that the area of the circle is greaterthan that of the rectangle by 104.5 cm2. Find the length of the wire.

Answer»

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