Question

# If a,b and c represent the lengths of sides of a triangle, then the possible integral value of ab+c+bc+a+ca+b is

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Solution

## We know, 0<a<b+c⇒ab+c<1(Triangle Inequality) ∴ab+c+bc+a+ca+b<3 In the case of a=b=c, we have ab+c=12 ⇒32≤ab+c+bc+a+ca+b<3 ∴ Integral values of ab+c+bc+a+ca+b=2

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