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

 

 

 

Answer:

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

Given,

∆ ABC ~ ∆ DEF.

The ratio of areas of two similar triangles is equal to the ratio of squares of their corresponding altitudes.

\frac{a \times(\triangle A B C)}{ar(\triangle D E F)}=\frac{(A P)^{2}}{(D Q)^{2}}

\frac{\operatorname{ar}(\triangle A B C)}{\operatorname{ar}(D E F)}=\frac{6^{2}}{9^{2}}

\Rightarrow \frac{36}{81}

\Rightarrow \frac{4}{9}

The ratio of their areas is 4 : 9