Question:
If the altitude of two similar triangles are in the ratio 2 : 3, what is the ratio of their areas?
Solution:
GIVEN: Altitudes of two similar triangles are in ratio 2:3.
TO FIND: Ratio of the areas of two similar triangles.
Let first triangle be ΔABC and the second triangle be ΔPQR
We know that the areas of two similar triangles are in the ratio of the squares of the corresponding altitudes.
$\Rightarrow \frac{\text { Area }(\mathrm{ABC})}{\text { Area }(\mathrm{PQR})}=\frac{2^{2}}{3^{2}}$
$\frac{\text { Area }(\mathrm{ABC})}{\text { Area }(\mathrm{PQR})}=\frac{4}{9}$