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?
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)
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