Question

Constructing the Third Side of a Triangle
A student is constructing a triangle with the following dimensions:

side length of 10 inches

side length of 30 inches

Which measurements could be the length of the third side? Select all that apply.
19 inches
21 inches
35 inches
45 inches
50 inches

Answer 1

Use the triangle inequality: the third side x must satisfy |30 − 10| < x < 30 + 10, i.e. 20 < x < 40.
From the choices only 21 and 35 lie between 20 and 40, so those two are possible.