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Question

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

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Solution

Given,
A wire is bent in shape of rectangle with length a & breadth b.
According to question
[a=2b]
Area of rectangle =l×b=a×a2=a22 ………..(1)
The same wire is bent in shape of circle.
Area of circle =πr2
where r=2(a+b)2π=3a2π
[Perimeter of rectangle = Perimeter of circle]
Area of circle =π×9a24π2=9a24π ………..(2)
Given area of circle = area of rectangle +104.5
9a24π=a22+104.5
a2[94π12]=104.5
a2[0.21]=104.5
[a=22.30cm]b=22.302=11.15cm
Hence length of wire =2(a+b)
=2(22.30+11.15)
=2(33.45)
Length =99.90100
Hence wire is 100 cm long.

1183170_1358668_ans_fbe900936fd44885b0016a9c4427a5c5.JPG

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