Question

A rectangular carpet has an area of 60 sq. m. 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 1

Answer: (B)

$12$ m

The answer is option $B$

Diagonal $=D=\sqrt{Lenght{h}^2+Breadt{h}^2}=\sqrt{L^2+B^2}$

$\Rightarrow D^2=L^2+B^2$

It's given that Area $=60$

$\Rightarrow LB=60$

Also given that $D+L=5\times B$

$\Rightarrow D=5B-L$

Squaring both sides,

$D^2=(5B-L{)}^2=25B^2-10LB+L^2$

$\Rightarrow L^2+B^2=25B^2-10LB+L^2$

$\Rightarrow 24B^2=10LB$

$\Rightarrow 24B^2=10\times 60=600$

$\Rightarrow B^2=25$

$\Rightarrow B=5$

$\Rightarrow L=60/B=60/5=12$