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:
5m
12m
13m
14.5m
Explanation:
Let, length= x meters and breadth= y meters
Then xy=60 and $(x^2+y^2) $+ x= 5
Therefore, x=60 and $(x^2 + y^2)$ = $(5y-x) ^2$.
Or xy=60 and $24y^2$-10xy = 0.
Therefore, $24y^2$ - 10 $\times$ 60 = 0 or
=> $y^2$ = 25
=> y = 5.
Therefore, x= (60/5) m= 12m.
So, length of the carpet = 12m