Question

The ratio of the areas of two triangles with the common base is 6 : 5. Height of the larger triangle is 9 cm. Then find the corresponding height of the smallest triangle.

Answer 1

In two triangles with the common base, we have A₁:A₂ = 6:5 and h₁ = 9 cm.
We know that the ratio of the areas of two triangles with the same base is equal to the ratio of their corresponding heights.
Thus, we get:

$$\begin{gathered} \frac{A_1}{A_2}=\frac{h_1}{h_2} \\ \Rightarrow \frac{6}{5}=\frac{9}{h_2} \\ \Rightarrow h_2=7.5\mathrm{cm} \end{gathered}$$

Therefore, the height of the smaller triangle is 7.5 cm.