Subject: General Aptitude · Chapter: Area · Exam: 2007 · Marks: · Difficulty:
The diagonal of a rectangular field is 15 metres and the difference between its length and width is 3 metres. The area of the rectangular field is
(a)$9 \mathrm{m}^{2}$
(b)$12 \mathrm{m}^{2}$
(c)$21 \mathrm{m}^{2}$
(d)$108 \mathrm{m}^{2}$
Answer
Answer (as printed):
Explanation
Let $l$ and $b$ be the length and breadth of the rectangle respectively. Then, $\sqrt{l^{2}+b^{2}}=15 \Rightarrow\left(l^{2}+b^{2}\right)=(15)^{2}=225$. $$\text { And, } \begin{aligned} l+b=3 & \Rightarrow(l-b)^{2}=9 \Rightarrow l^{2}+b^{2}-2 l b=9 \\ & \Rightarrow 225-2 l b=9 \Rightarrow 2 l b=216 \Rightarrow l b=108 . \end{aligned}$$ Hence, area of the field $=l b=108 \mathrm{m}^{2}$.