Question

A wire is bent in the form of a rectangle having twice the breadth the same wire is bent in the form of a circle it was found that area of the circle is a greater than that of a rectangle by 10 4.5 CM square find the length of the wire

Answer 1

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Answer:

66 cm

Step-by-step explanation:

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 of the wire:

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

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