Question 93

# Triangle ΔXYZ is similar to ΔPQR. If XY:PQ=5:1. If Area of ΔPQR is 5 sq cm, what is the area (in sq cm) of ΔXYZ?

Solution

Given : $$\triangle XYZ \sim \triangle PQR$$ and XY:PQ=5:1

To find : ar($$\triangle$$ XYZ) = $$x$$ = ?

Solution : Ratio of areas of two similar triangles is equal to the ratio of square of the corresponding sides.

=> $$\frac{ar(\triangle XYZ)}{ar(\triangle PQR)}=(\frac{XY}{PQ})^2$$

=> $$\frac{x}{5}=(\frac{5}{1})^2$$

=> $$\frac{x}{5}=\frac{25}{1}$$

=> $$x=25\times5=125$$ $$cm^2$$

=> Ans - (A)