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

Solution(By Examveda Team)

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