Question

If the ratio between the areas of these two triangles is $16:25$, find the ratio between their corresponding altitudes.

Answer 1

Let $ABC$ and $PQR$ be two isosceles triangles.

$\Rightarrow \frac{AB}{AC}=\frac{PQ}{PR}$

Also,$\angle A=\angle P$(given)

$\therefore △ABC\sim △PQR$ by SAS similarity

Let $AD$ and $PS$ be the altitude in the respective triangles.

We know that the ratio of areas of two similar triangles is equal to the square of their corresponding altitudes.

$\frac{Area\left(△ABC\right)}{Area\left(△PQR\right)}={\left(\frac{AD}{PS}\right)}^2$

$\Rightarrow \frac{16}{25}={\left(\frac{AD}{PS}\right)}^2$

$\therefore \frac{AD}{Ps}=\frac{4}{5}$