A triangle has two side of length 12.7 and 8.8. What compound inequality describes the possible lengths for the third side

Answer 1

The Triangle Inequality Theorem says that, given two side lengths of a triangle, the length of the third side of the triangle must be larger than the difference and smaller than the sum of the two given sides. For two sides a and b of a triangle, the third side c must follow the following:

(a - b) < c < (a + b)

Therefore, let a = 12.7 and b = 8.8:

(12.7 - 8.8) < c < (12.7 + 8.8)

3.9 < c < 21.5

Therefore, the third side of the triangle must follow the inequality 3.9 < c < 21.5.