A rectangular carpet has an area of 60 sq.m. If its diagonal and longer side together equal 5 times the shorter side, the length of the carpet is :

A. 5 m

B. 12 m

C. 13 m

D. 14.5 m

Answer: Option B

Solution(By Examveda Team)

We have :
$$lb$$ = 60 and $$\sqrt {{l^2} + {b^2}} + l = 5b$$
Now,
$$\eqalign{ & {l^2} + {b^2} = {\left( {5b - l} \right)^2} \cr & \Rightarrow 24{b^2} - 10lb = 0 \cr & \Rightarrow 24{b^2} - 600 = 0 \cr & \Rightarrow {b^2} = 25 \cr & \Rightarrow b = 5 \cr & \therefore l = \left( {\frac{{60}}{b}} \right) \cr & \,\,\,\,\,\,\,\, = \left( {\frac{{60}}{5}} \right)m \cr & \,\,\,\,\,\,\,\, = 12\,m \cr} $$
So, length of the carpet = 12 m