In the adjoining figure, $$ABCD$$ is a rectangle, and $$AE$$ and $$CF$$ are quadrants. The length of the rectangle is twice its breadth. Taking $$\pi=\frac{22}{7}$$, the shaded area is $$21\text{ cm}^2$$. The area of the rectangle is
[image]
Correct Answer: 98
Solution
Let the breadth be $$x$$, so the length is $$2x$$ and the rectangle area is $$2x^2$$. The two quadrants together have area $$\frac{\pi x^2}{2}=\frac{11x^2}{7}$$. Thus $$2x^2-\frac{11x^2}{7}=21$$, giving $$x^2=49$$ and rectangle area $$2x^2=98$$.
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