Question:
AM is a median of a triangle ABC. Is AB + BC + CA > 2 AM? (Consider the sides of triangles ΔABM and ΔAMC.)
AM is a median of a triangle ABC. Is AB + BC + CA > 2 AM? (Consider the sides of triangles ΔABM and ΔAMC.)
Updated On: Dec 8, 2023
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Solution and Explanation
In a triangle, the sum of the lengths of either two sides is always greater than the third side.
In \(ΔABM\),
\(AB + BM > AM\) (i)
Similarly, in \(ΔACM\),
\(AC + CM > AM\) (ii)
Adding equation (i) and (ii),
\(AB + BM + MC + AC > AM + AM\)
\(AB + BC + AC > 2\;AM\)
Yes, the given expression is true.
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