Subject: General Aptitude · Chapter: Area · Exam: · Marks: · Difficulty:
A rectangular carpet has an area of $120 \mathrm{m}^{2}$ and a perimeter of 46 metre. The length of its diagonal is
(a)23 metre
(b)13 metre
(c)17 metre
(d)21 metre [SSC-CHSL (10+2) Exam, 2015]
Answer
Answer (as printed): C
Explanation
Let the length of carpet be $l$ meter and breadth the $b$ meter. $$\text { ∴ } \text { Diagonal }=\sqrt{l^{2}+b^{2}}$$ According to the question, $l b=120$ and $2(l+b)=46$ $\Rightarrow l+b)=23$ On squaring both sides. $$\begin{aligned} & (l+b)^{2}=23^{2} \\ & \Rightarrow l^{2}+b^{2}+2 l b=529 \\ & \Rightarrow l^{2}+b^{2}+2 \times 120=529 \\ & \Rightarrow l^{2}+b^{2}=529-240=289 \\ & \therefore \sqrt{l^{2}+b^{2}}=\sqrt{289}=17 \end{aligned}$$ Diagonal of the carpet $=17 \mathrm{m}$