Question

The area of two similar triangle are $81$ $c{m}^2$cm2 and $49c{m}^2$ respectively. Find ratio of their corresponding heights. What is the ratio of their corresponding medians?

Answer 1

Since the ratio of the areas of two similar triangles is equal to the ratio of the squares of their corresponding altitudes and is also equal to the ratio of squares of their corresponding medians.

$\therefore$ $\frac{Areaoftriangle1}{Areaoftriangle2}={\left(\frac{H_1}{H_2}\right)}^2$

$\therefore$ $\frac{81}{49}={\left(\frac{H_1}{H_2}\right)}^2$

$\therefore$ $\frac{H_1}{H_2}=\frac{9}{7}$

$\therefore$ Ratio of corresponding heights is $9:7$ and ratio of corresponding medians is also $9:7$