Question

∆ABC~∆PQR. If AM and PN are altitudes of ∆ABC and ∆PQR respectively and AB2 :  PQ2 = 4 : 9, then AM:PN = (a) 16:81 (b) 4:9 (c) 3:2 (d) 2:3​

Answer 1

Step-by-step explanation:

∆ABC~∆PQR. If AM and PN are altitudes of ∆ABC and ∆PQR respectively and AB2 :  PQ2 = 4 : 9, then AM:PN = (a) 16:81 (b) 4:9 (c) 3:2 (d) 2:3

16:81

Answer 2

Step-by-step explanation:

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

To find: AM:PN

(a) 16:81

(b) 4:9

(c) 3:2

(d) 2:3

Solution:

We know that when two triangles are similar then ratio of their sides are equal.

$\frac{AB^2}{PQ^2}=\frac{4}{9}$

or

$\frac{AB^2}{PQ^2}=\frac{2^2}{3^2}$

or

$\left(\frac{AB}{PQ}\right)^2=\left(\frac{2}{3}\right)^2$

taking square root both sides

$\frac{AB}{PQ}=\frac{2}{3}$

When two triangles are similar than ratio of their altitudes are equal to ratio of their sides.

Thus,

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

So,

Ratio of altitudes

$\frac{AM}{PN}=\frac{2}{3}$

Option D is correct.

Final answer:

$\bold{\pink{\frac{AM}{PN}=\frac{2}{3}}}$

Option D is correct.

Hope it helps you.

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