5. AM is a median of a triangle ABC. Is AB + BC + CA > 2 AM?
(Consider the sides of triangles ΔABM and ΔAMC.)
6. ABC is a triangle right angled at C. If AB = 25 cm and AC = 7 cm, find BC.
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5. we know,
In a triangle sum of two sides is greater than the third side
Hence,In triangle ABM
AB + BM > AM .........1
Also in triangle ACM
AC + MC > AM ..........2
Adding equation 1 and 2 we get,
AB + BM + AC + MC > AM + AM
AB + AC + (BM + MC) > 2AM
AB + AC + BC > 2AM
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