Question 5

The perimeter of a rectangle is 240 cm. If its length is increased by $$10\%$$ and its breadth is decreased by $$20\%$$, the perimeter remains the same. The length and breadth of the original rectangle respectively are

Solution

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From the perimeter, $$l + b = 120$$. Since the perimeter is unchanged, $$1.1l + 0.8b = 120$$, so $$0.1l = 0.2b$$ and $$l = 2b$$. Then $$3b = 120$$, giving $$b = 40$$ cm and $$l = 80$$ cm.

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