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Question

Question 96

Solve the following:

The perimeter of a rectangle is 240cm. If its length is is increased by 10% and its breadth is decreased by 20%, then we get the same perimeter. Find the length and breadth of the rectangle.

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Solution

Given, perimeter of rectangle =240m
2×(Length+Breadth)=240 cm
Length+Breadth=120 cm
Let the length of rectangle be x cm.
Then, the breadth of rectangle =(120-x) cm
New length of rectangle =x+10% of x=x+ 10100×x=110100 x cm
(120x)20100×(120x) (120x)(120100)=80100(120x)cm
It is given that, perimeter of new rectangle is 240 cm.
According to the question,
2×(New length+New breadth)=240
2×[110x100+80100(120x)]=240110x+960080x100=240230x+9600=2402×10030x+9600=1200030x=12000960030x=2400x=240030=80
Hence, length of rectangle=80cm
and breadth of rectangle=120-80=40cm.


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