Subject: General Aptitude · Chapter: Area · Exam: · Marks: · Difficulty:
The length of a rectangle is three times of its width. If the length of the diagonal is $8 \sqrt{10} \mathrm{cm}$, then the perimeter of the rectangle is
(a)$15 \sqrt{10} \mathrm{cm}$
(b)$16 \sqrt{10} \mathrm{cm}$
(c)$24 \sqrt{10} \mathrm{cm}$
(d)64 cm
Answer
Answer (as printed):
Explanation
Let breadth $=x \mathrm{cm}$. Then, length $=3 x \mathrm{cm}$. $$x^{2}+(3 x)^{2}=(8 \sqrt{10})^{2} \Rightarrow 10 x^{2}=640 \Rightarrow x^{2}=64 \Rightarrow x=8 .$$ So, length = 24 cm and breadth = 8 cm. $$\therefore \text { Perimeter }=[2(24+8)] \mathrm{cm}=64 \mathrm{cm} .$$