Question

The corresponding altitudes of two similar triangles are 6 cm and 9 cm respectively. Find the ratio of their areas.

Answer 1

Let the two triangles be ABC and DEF with altitudes AP and DQ, respectively. 

  

It is given that Δ ABC ~ Δ DEF.
We know that the ration of areas of two similar triangles is equal to the ratio of squares of their corresponding altitudes. 

`(ar(ΔABC))/(ar(ΔDEF))=(AP)^2/(DQ)^2` 

⇒ `(ar(ΔABC))/(ar(ΔDEF))=6^2/9^2` 

=`36/81` 

=`4/9` 

Hence, the ratio of their areas is 4 : 9