Question

The corresponding altitudes of two similar triangles are 3 cm and 5 cm respectively. Find the ratio between their areas.

Answer 1

As shown in the above figure, let $△ABC$ and $△DEF$ be the similar triangles with altitudes $AM$ and $DN$ and with $AM\perp BC$ and $DN\perp EF$.

We know that the arc of similar triangles are proportional to squares of their corresponding altitude, therefore with the given altitudes $3$ cm and $5$ cm, we have,

$\frac{Ar(△ABC)}{Ar(△DEF)}=\frac{A{M}^2}{D{N}^2}=\frac{3^2}{5^2}=\frac{9}{25}$

Hence the ratio between the areas is $9:25$.