The sum of the length and breadth of a rectangle is $$6\text{ cm}$$. A square is constructed whose side is equal to the diagonal of the rectangle. If the ratio of the areas of the square and the rectangle is $$\frac{5}{2}$$, then the area of the square in $$\text{cm}^2$$ is
Correct Answer: 20
Solution
Let the rectangle sides be $$l$$ and $$b$$. The square area is $$l^2+b^2$$, and the given ratio gives $$l^2+b^2=\frac{5}{2}lb$$. Since $$(l+b)^2=36=l^2+b^2+2lb$$, we obtain $$36=\frac{9}{2}lb$$ and hence $$lb=8$$. Therefore, the square area is $$\frac{5}{2}\times 8=20$$.
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