Question

a triangle with points a, b, c. ab is 12, ac is 15, bc is x (dotted line). the value of x must be greater than ______. options: 0, 1, 3, 7

Explanation:

Step1: Apply triangle inequality

The sum of two sides > third side: $12 + x > 15$, $15 + x > 12$, $12 + 15 > x$.

Step2: Solve for x

From $12 + x > 15$: $x > 3$. Other inequalities give $x > -3$ (irrelevant) and $x < 27$. So x > 3.

Answer:

C. 3