If AM and PN are altitudes of and respectively and = 4 : 9, then AM : PN =

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Solution

Q.
$ΔABC ~ ΔPQR$ . If AM and PN are altitudes of $ΔABC$ and $ΔPQR$ respectively and $A B^{2} : P Q^{2}$ = 4 : 9, then AM : PN =

1 3 : 2

2 16 : 81

3 4 : 9

4 2 : 3

Ans.
(4)

We have, $∆ A B C ~ ∆ P Q R$

$\Rightarrow \frac{A B}{P Q} = \frac{B C}{Q R} = \frac{C A}{R P} = \frac{A M}{P N} (corresponding sides of similar triangles)$

But $\frac{A B^{2}}{P Q^{2}} = \frac{4}{9} \Rightarrow \frac{A B}{P Q} = \frac{2}{3}$

i.e., $\frac{A B}{P Q} = \frac{A M}{P N} = \frac{2}{3}$

Hence, $A M : P N = 2 : 3$

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