Subject: General Aptitude · Chapter: Area · Exam: · Marks: · Difficulty:
In the given diagram, $A B C D$ is a square and semi-circular regions have been added to it by drawing two semicircles with $A B$ and $C D$ as $5 \sqrt{7} \mathrm{cm}$
(b)7 cm
(c)13 cm
(d)14 cm
Answer
Answer (as printed): D
Explanation
Let the length of the side of the square be $x \mathrm{cm}$. Then, radius of each semi circle $=\left(\frac{x}{2}\right) \mathrm{cm}$. $$\begin{aligned} & \text { Total area }=\left[x^{2}+\frac{\pi}{2}\left(\frac{x}{2}\right)^{2}+\frac{\pi}{2}\left(\frac{x}{2}\right)^{2}\right] \mathrm{cm}^{2} \\ & \quad=\left(x^{2}+\frac{\pi}{4} x^{2}\right) \mathrm{cm}^{2} . \\ & \therefore x^{2}+\frac{\pi}{4} x^{2}=350 \Rightarrow x^{2}+\frac{22 x^{2}}{28}=350 \\ & \quad \Rightarrow x^{2}+\frac{11 x^{2}}{14}=350 \\ & \quad \Rightarrow \frac{25 x^{2}}{14}=350 \Rightarrow x^{2}=\left(\frac{350 \times 14}{25}\right)=196 \\ & \quad \Rightarrow x=14 \mathrm{cm} . \end{aligned}$$