∆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
(d) 2:3
Explanation:
Given,
= `"AB"^{2}` : `"PQ"^{2}"`
= `frac{4}{9}`
= `("AB"^{2}/"PQ"^{2}")` = `("2"/"3")^{2}"`
= `"AB"/"PQ"` = `frac{2}{3}`
When two triangles are similar
Ratio of their altitudes = Ratio of their sides
= `"AM"/"PN"` = `"AB"/"PQ"`
= `"AM"/"PN"` = `"2"/3"`
= AM:PN = 2:3
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