Question

if 2 triangles are similar such that ratio of their areas is 25:361 ratio of their corresponding medians is​

Answer 1

Solution:

Keep in mind this theorem

Area of two similar triangles is equal to ratio of square of their corresponding sides as well as median.

Let, $A_{1},A_{2}$ be two similar triangles.And,a and b be the corresponding length of Median.

$\frac{A_{1}}{A_{2}}=\frac{a^2}{b^2}\\\\ \frac{25}{361}=\frac{a^2}{b^2}\\\\ \frac{5^2}{19^2}=\frac{a^2}{b^2}\\\\ (\frac{5}{19})^2=(\frac{a}{b})^2\\\\ \frac{a}{b}=\frac{5}{19}$

Ratio of Corresponding Median will be = 5:19