Krishna
0

Step 1:  Recall the relation between the areas of the similar triangles.

            THEOREM: The ratio of the areas of two similar triangles is equal to the

            ratio of the squares of their corresponding sides

             \frac{Area \triangle ABC}{Area \triangle DEF} = (\frac{AB}{DE})^2 = (\frac{BC}{EF})^2 = (\frac{CA}{FD})^2   

             And also,  \frac{Area\ \triangle ABC}{Area\ \triangle DEF}=(\frac{Altitude\ 1}{Altitude\ 2})^2 


Step 2: Substitute all the known values in the theorem

            EXAMPLE:  \frac{81}{49}=(\frac{4.5}{Altitude\ 2})^2                                

                         \Rightarrow\ Altitude\ 2\ =\ \sqrt{\left(4.5\right)^2\cdot\frac{49\ }{81}}

                        

                          \Rightarrow Altitude\ 2\ =\ 4.5\ \frac{7}{9}

                      Altitude of a smaller triangle = 3.5 cm