Question

The ratio of the areas of two triangles with common base is $6:5$. Height of the larger triangle is $9$cm, then find the corresponding height of the smaller triangle.

Answer 1

Let the areas of the larger and the smaller triangle be $A_1$ and $A_2$ respectively. Let their heights be $h_1$ and $h_2$ respectively.

Given $\frac{A_1}{A_2}=\frac{6}{5},h_1=9$ and the two triangles have the common base.

$\therefore \frac{A_1}{A_2}=\frac{h_1}{h_2}$

$\Rightarrow \frac{6}{5}=\frac{9}{h_2}$

$\Rightarrow h_2=\frac{45}{6}$

$\Rightarrow h_2=7.5cm$

Thus the height of the smaller triangle is $7.5cm$