A rectangular carpet has an area of 120 m2 and a perimeter of 46 metres. The length of its diagonal is :

Answer: Option C

Let the length of carpet be l metres and breadth the b metres
∴ Diagonal = $$\sqrt{l^2+b^2}$$
According to the question,
$$\begin{array}{rl}& lb=120\text{ and }\text{2}\left(l+b\right)=46\\ & \Rightarrow \left(l+b\right)=23\end{array}$$
On squaring both sides :
$$\begin{array}{rl}& \Rightarrow {\left(l+b\right)}^2=23^2\\ & \Rightarrow l^2+b^2+2lb=529\\ & \Rightarrow l^2+b^2+2\times 120=529\\ & \Rightarrow l^2+b^2=529-240\\ & \Rightarrow l^2+b^2=289\\ & \therefore \sqrt{l^2+b^2}=\sqrt{289}=17\end{array}$$
Diagonal of the carpet = 17 metres