Question

If the altitude of two similar triangles are in the ratio 2:3, what is the ratio of their areas?

Answer 1

Area of Triangle $\propto$ Height of triangle

as $Area=\frac{1}{2}base\ast height$

Since the Triangle are Similar

Ratio of all sides of both Triangles will be same

Hence, $\frac{h_1}{h_2}=\frac{b_1}{b_2}=\frac{2}{3}$

So, Ratio of Area $=\frac{\frac{1}{2}{h}_1{b}_1}{\frac{1}{2}{h}_2{b}_2}=\frac{h_1}{h_2}\ast \frac{b_1}{b_2}=\frac{2}{3}\ast \frac{2}{3}=\frac{4}{9}$