EXAMPLE 3 Find possible side lengths ALGEBRA A triangle has one side of length 12 and another of length 8. Describe the possible lengths of the third side.

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EXAMPLE 3 Find possible side lengths ALGEBRA A triangle has one side of length 12 and another of length 8. Describe the possible lengths of the third side. SOLUTION Let x represent the length of the third side. Draw diagrams to help visualize the small and large values of x. Then use the Triangle Inequality Theorem to write and solve inequalities.

EXAMPLE 3 Find possible side lengths Small values of x Large values of x x + 8 > 12 x > > x 20 >x,x, or x < 20 The length of the third side must be greater than 4 and less than 20. ANSWER

GUIDED PRACTICE for Example 3 3. A triangle has one side of 11 inches and another of 15 inches. Describe the possible lengths of the third side. SOLUTION Let x represent the length of the third side. Draw diagrams to help visualize the small and large values of x. Then use the Triangle Inequality Theorem to write and solve inequalities. Small values of x x Large values of x x x + 11 > 15 x > > x x >26 4 < x < 26 The length of the third side is