Question

∆ABC~∆PQR. If AM and PN are altitudes of ∆ABC and ∆PQR respectively and AB2 : PQ2 = 4 : 9, then AM:PN =​

Answer 1

Given:

$\[\Delta ABC \sim \Delta PQR\]$ and $\[A{B^2}:P{Q^2} = 4:9\]$

Solution:

Know that the ratio the sides of the two similar triangles is equal to the ratio of their corresponding sides.

Therefore,

$\[\frac{{AM}}{{PN}} = \frac{{AB}}{{PQ}}\]$

Find AB:PQ,

$\[\begin{array}{l} \Rightarrow \frac{{AB}}{{PQ}} = \sqrt {\frac{4}{9}} \\ \Rightarrow \frac{{AB}}{{PQ}} = \frac{2}{3}\end{array}\]$

So that,

$\[AM:PN = 2:3\]$

Hence, the ratio of AM to PN is 2:3.