Question

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

Answer 1

Answer:

66cm

Step-by-step explanation:

Define x:

Let the breadth be x

The length = 2x

Find the perimeter of the rectangle:

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

Find the circumference of the circle:

Circumference = Perimeter = 6x

Find the radius:

Radius = 2πr ÷ 2π

Radius = 6x ÷ 2π

Radius = 3x/π

Find the area of the circle:

Area = πr²

Areas = π(3x/π)²

Area = 9x²/π cm²

Find the area of the rectangle:

Area = Length x Breadth

Area = (2x)(x) = 2x² cm²

Solve x:

Given that the difference is 104.5 cm²

9x²/π - 2x² = 104.5

19/22 x² = 104.5

x² = 121

x = √121

x = 11 cm

Find the length of the wire:

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

Answer: The length is 66 cm

Answer 2

heya

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