Question

Triangle ABC ~ Triangle PQR. If AM and PN are altitudes of Triangle ABC and Triangle PQR respectively and (AB)2:(PQ)2=4:9, then AM: PN=


(A)16:81 (B)4:9 (C)3:2 (D)2:3

Answer 1

Answer:

Correct answer is: (d) 2:3 Ratio of altitudes = Ratio of sides for similar triangles So AM:PN = AB:PQ = 2:3

Since ratio of similar triangles are in ratio of squares of their corresponding sides ar(∆ABC)/ ar(∆PQR) = (AB/PQ)² = 4/9 Also, ratio of similar triangles are in ratio of squares of their corresponding altitudes. (AM/PN)² = 4/9 AM/PN = 2/3 Hence, option (d) is correct

Step-by-step explanation:

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