CAT 2021

Slot 3

QA

Question & Solution

We can say 40m is the perimeter of the park 
so side of rhombus = 10 
Now $\frac{1}{2}\times\ d_1\times\ d_2\ =\ 96$
so we get $\ d_1\times\ d_2\ =\ 192$   (1)
And as we know diagonals of a rhombus are perpendicular bisectors of each other :
so $\ \frac{d_1^2}{4}+\ \frac{d_2^2}{4}=\ 100$
so we get $\ d_1^2+\ d_2^2=\ 400$    (2)
Solving (1) and (2)
We get $d_1=12$ and$d_2=16$
Now the cost, in INR, of laying electric wires along its two diagonals, at the rate of ₹125 per m, is= (12+16)(125) =3500