[12m] A rectangular carpet has an area of 60 sq.m. If its diagonal and longer side together equal 5 times

For Competitive Exams

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:

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

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Robert Bosch Logical Reasoning Test