Question

Two isosceles triangles have equal angles and their areas are in the ratio 16: 25. The ratio of their corresponding heights is

• A. 4 : 5
• B. 5 : 4
• C. 3 : 2
• D. 5 : 7

Answer 1

The correct option is A 4 : 5

Let the required triangle be $\Delta ABCand\Delta PQR$

with $\angle A=\angle P$

So $\Delta ABC$ is similar to $\Delta PQR$

(By SAS similarity)

Let the altitude of two triangles be AD and PS

So The ratio of the areas of two similar triangle is equal to the square of ratio of their corrosponding altitudes.

$\frac{ar\left(\Delta ABC\right)}{ar\left(\Delta PQR\right)}=\frac{A{D}^2}{P{S}^2}$

$\to \frac{16}{25}=\frac{A{D}^2}{P{S}^2}$

$\to \frac{AD}{PS}=\frac{4}{5}=4:5$