The two sides of a triangle are 0.5 and 7.9, respectively. What integer can be the length of the third side?

Let’s denote the sides of the triangle as a, b, c. For any triangle the following inequalities are true: a + b> c; a + c> b; b + c> a. Let a = 0.5; в = 7.9, then we apply the above written inequalities for the sides of any triangle, we get: 0.5 + 7.9> c; 8.4> c. Hence, c <= 8.

But further, you need to apply other inequalities: a + c> b; b + c> a;

0.5 + c> 7.9; 7.9 + c> 0.5. The second inequality is valid for any c, and for the first inequality only c = 8 is suitable, and for c = 7, the inequality does not hold.

Answer: c = 8.