Question

Ratio of areas of two triangles with equal heights is 2 : 3. If base of the smaller triangle is 6 cm then what is the corresponding base of the bigger triangle ?

Answer 1

$$\begin{gathered} \frac{\mathrm{Area}\mathrm{of}\mathrm{smaller}\mathrm{triangle}}{\mathrm{Area}\mathrm{of}\mathrm{bigger}\mathrm{triangle}}=\frac{2}{3} \\ \Rightarrow \frac{{\displaystyle \frac{1}{2}}{\displaystyle \times }\mathrm{Height}\mathrm{of}\mathrm{smaller}\mathrm{triangle}\times \mathrm{Base}\mathrm{of}\mathrm{smaller}\mathrm{triangle}}{{\displaystyle \frac{1}{2}}\times \mathrm{Height}\mathrm{of}\mathrm{bigger}\mathrm{triangle}\times \mathrm{Base}\mathrm{of}\mathrm{bigger}\mathrm{triangle}}=\frac{{\displaystyle 2}}{{\displaystyle 3}} \\ \Rightarrow \frac{{\displaystyle 6}}{{\displaystyle \mathrm{Base}\mathrm{of}\mathrm{bigger}\mathrm{triangle}}}=\frac{{\displaystyle 2}}{{\displaystyle 3}} \end{gathered}$$
$$\begin{gathered} \Rightarrow \mathrm{Base}\mathrm{of}\mathrm{bigger}\mathrm{triangle}=\frac{{\displaystyle 3}}{{\displaystyle 2}}\times 6 \\ =9 \end{gathered}$$