Question 20

$$PQRS$$ is a square. The sides $$PQ$$ and $$RS$$ are increased by 30 % each and the sides $$QR$$ and $$PS$$ are increased by 20 % each. The area of the quadrilateral thus obtained exceeds the area of the square by _________ %.

Correct Answer: 56

Solution

If the square has side $$a$$, its area is $$a^2$$ and the new rectangle has sides $$1.3a$$ and $$1.2a$$. Its area is $$1.3a \times 1.2a = 1.56a^2$$. The excess is $$0.56a^2$$, which is 56 % of the original area.

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