Question

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

Answer 1

Answer:

16:81

Step-by-step explanation:

Since the areas of two similar triangles are in the ratio of the squares of the corresponding altitudes.

∴ Area(△PQR)Area(△ABC)=PS2AD2

⇒ Area(△PQR)Area(△ABC)=(94)2=8116              [∵AD:PS=4:9]

⇒ Area(△PQR)Area(△ABC) = 1681

pls mark BRAINLIEST

♥️♥️♥️♥️♥️ ⭐⭐⭐⭐⭐

Answer 2

Given:

$\[\Delta ABC \sim \angle PQR\]$

Solution:

Know that, In a similar triangle the ratio of the heights and length of sides are in the same proportion.

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

Find the ratio of the sides,

$\[\frac{{A{B^2}}}{{P{Q^2}}} = \frac{4}{9}\]$

$\[ \Rightarrow \frac{{AB}}{{PQ}} = \sqrt {\frac{4}{9}} \]$

$\[ \Rightarrow \frac{{AB}}{{PQ}} = \frac{2}{3}\]$

So that, $\[\frac{{AM}}{{PN}} = \frac{2}{3}\]$

Hence, $\[\frac{{AM}}{{PN}} = \frac{2}{3}\]$