Question

a wire is bent in the form of a rectangle having length twice the breath the same wire is bent in the form of circle it was found that area of circle is greaterthan that of rectangle by 104.5 CM square find the length of wire

Answer 1

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$<b>Answer:</b>$

66 cm

$<b>Step-by-step explanation:</b>$

$<u>Define x:</u>$

Let the breadth be x

The length is 2x

Find the Perimeter of the rectangle:

Perimeter = 2(Length + Breadth)

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

Find the area of the rectangle:

Area = Length x Breadth

Area = 2x(x) = 2x²

Find the radius of the circle:

Circumference = 2πr

6x = 2πr

r = 6x ÷ 2π

r = 3x/π

Find the area of the circle:

Area = πr²

Area = π(3x/π)²

Area = 9x²/π

Area =63x²/22

Solve x:

Give that the area circle is 104.5 cm² greater than the rectangle.

63x²/22 -  2x² = 104.5

63x² - 44x² =  2299

19x² = 2299

x² = 121

x = √121

x = 11 cm

Find the perimeter of the wire:

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

Answer: The perimeter is 66 cm long.

$\large{\sf{Regards\: by \: @avinashsingh31}}$

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