In a triangle ABC, let D be the midpoint of BC, and AM be the altitude on BC. If the lengths of AB, BC and CA are in the ratio of 2:4:3, then the ratio of the lengths of BM and AD would be
Question and options
In a triangle ABC, let D be the midpoint of BC, and AM be the altitude on BC. If the lengths of AB, BC and CA are in the ratio of 2:4:3, then the ratio of the lengths of BM and AD would be
Answer and explanation
Correct answer: A - \(11:4\sqrt{10}\)
Take AB=2, BC=4, CA=3. BM = (AB^2+BC^2-CA^2)/(2BC) = (4+16-9)/8 = 11/8. Median AD^2 = (2*4+2*9-16)/4 = 10/4, AD = sqrt10/2. BM:AD = (11/8)/(sqrt10/2) = 11:4sqrt10.
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IPMAT Indore
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