Question

Select each of the following that are valid triangles by the Triangle Inequality. Make multiple selections if there is more than one correct answer.

A. Triangle with side lengths 17, 8, and 23.

B. Triangle with side lengths 7, 23, and 14.

C. Triangle with side lengths 11, 23, and 30.

D. Triangle with side lengths 23, 8, and 12.

Answer 1

A, C

Explanation:

The triangle inequality requires the sum of the shortest sides exceed the length of the longest side. We can find those sums to be ...

A. 8 + 17 = 25 > 23 . . . . . valid triangle

B. 7 + 14 = 21 < 23 . . . not

C. 11 + 23 = 34 > 30 . . . . . valid triangle

D. 8 + 12 = 20 < 23 . . . not

Choices A and C are valid triangles.