Question

Two sides of a triangle have lengths 5 and 7. Which inequalities represent the possible lengths for the third side, x?

a) 2 < x < 12
b) 12 < x < 14
c) 2 < x < 5
d) 5 < x < 7

Answer 1

The possible lengths for the third side, x, of a triangle with sides of lengths 5 and 7 can be found by using the Triangle Inequality Theorem. The correct inequality representing the possible lengths for x is 2 < x < 12.

Step-by-step explanation:

The possible lengths for the third side, x, of a triangle can be found using the Triangle Inequality Theorem. According to this theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. In this case, the given sides have lengths 5 and 7. Therefore, the possible lengths for the third side, x, would satisfy the inequality 5 + 7 > x. Simplifying that inequality, we get x < 12. So, the correct inequality is option a) 2 < x < 12.