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Question
The perimeter of a rectangle is 240 cm. If its length is increased by 10% and its breadth is decreased by 20%, we get the same perimeter. Find the length and breadth of the rectangle.
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Solution
Given, perimeter of rectangle = 240 cm
⇒ 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 + 10/100 xx x`
= `110/100 x cm`
And new breadth of rectangle = (120 – x) – 20% of (120 – x) cm
= `(120 - x) - 20/100 xx (120 - x)`
= `(120 - x)(1 - 20/100)`
= `80/100 (120 - x) cm`
It is given that, perimeter of new rectangle is 240 cm.
According to the question,
2 × (New length + New breadth) = 240
⇒ `2 xx [(110x)/100 + 80/100 (120 - x)] = 240`
⇒ `(110x + 9600 - 80x)/100 = 240/2`
⇒ `30x + 9600 = 240/2 xx 100`
⇒ 30x + 9600 = 12000
⇒ 30x = 12000 – 9600
⇒ 30x = 2400
⇒ x = `2400/30` = 80
Hence, length of rectangle = 80 cm
And breadth of rectangle = 120 – 80 = 40 cm.
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