Question

A rectangular carpet has an area of $60$ $m^2$. 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

Given Area of rectangular carpet $=60m^2$

$l\times b=60$ .....(1)
Also $l+d$ $=$ $5b$ ......(2)

Also by pythagoras theorem, we can say that $l^2+b^2=d^2$ .....(3)

From (2) and (3), we have

$l^2+b^2=(5b-l{)}^2$

$\Rightarrow l^2+b^2=25b^2+l^2-10lb$

$\Rightarrow 24b^2=10lb$

$\Rightarrow 24b^2=10\times 60$ .....(From 1)

$\Rightarrow b^2=25$

$\Rightarrow b=5$

$lb=60$ and $b=5\Rightarrow l=12$

So, length of carpet is $12$ m .