Question

# In the given triangle ABC, D is any point on side BC, then: AB+BC+AC>2ADA.TrueB.False

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Hint: We are going to solve the given problem using the triangular inequality of triangles. It gives the information that the sum of any two sides of a triangle is greater than the third side.

It is given in a triangle ABC, D is a point anywhere on BC. So when we put the point D on BC and joins that point from vertex A, triangle ABC will divide into two triangles, triangle ABD, triangle ACD
In triangle ABD,
AB+BD>AD [because, the sum of any two sides of a triangle is always greater than the third side]
AC+DC>AD [because, the sum of any two sides of a triangle is always greater than the third side]
$\Rightarrow$ AB + (BD + DC) + AC > 2AD
$\Rightarrow$ AB + BC + AC > 2AD