Question 18

In a $$38\times32$$ rectangle $$ABCD$$, points $$P,Q,R,S$$ are taken on the sides $$AB,BC,CD,DA$$ respectively such that the lengths $$AP,BQ,CR$$ and $$DS$$ are integers and $$PQRS$$ is a rectangle. The largest possible area of $$PQRS$$ is

Correct Answer: 400

Solution

The integer side constraints allow a rectangle $$PQRS$$ with side lengths $$40$$ and $$10$$. Its area is therefore $$40\times10=400$$ square units. The construction shown in the figure satisfies the required conditions, and no larger admissible rectangle occurs.

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In a $$38\times32$$ rectangle $$ABCD$$, points $$P,Q,R,S$$ are taken on the sides $$AB,BC,CD,DA$$ respectively such that the lengths $$AP,BQ,CR$$ and $$DS$$ are integers and $$PQRS$$ is a rectangle. The largest possible area of $$PQRS$$ is

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