Question

The areas of two similar triangles are $81{cm}^2$ and $49{cm}^2$ respectively. Find the ratio of their corresponding heights. What is the ratio of their corresponding medians?

Answer 1

For similar triangles,
Ratio of areas = Ratio of square of heights = Ratio of square of medians (Similar triangle property)
$\frac{(M_1{)}^2}{(M_2{)}^2}=\frac{(H_1{)}^2}{(H_1{)}^2}=\frac{81}{49}$
$\therefore \frac{M_1}{M_2}=\frac{H_1}{H_2}=\frac{9}{7}$