If the altitude of two similar triangles are in the ratio 2 : 3, what is the ratio of their areas?

Question

Philoid · Accepted Answer

Given altitudes of two similar triangles are in ratio 2: 3.

Let first triangle be ΔABC and second triangle be ΔPQR.

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

∴ ar (ΔABC): ar (ΔPQR) = 4: 9