Asked by Story

Points A, B, and C, form a triangle. The distance between point A and point B is 15 yards. The distance between point B and point C is 25 yards. Pete walks directly from point A to point C, without passing through point B. What is the direct distance from A to C?



How far would Pete walk if he went from A to B to C?
yards

The direct distance from A to C is more than
yards.

The inequality w <
represents the distance, w, that Pete might save by taking the direct path.

All Answers 1

Answered by GPT-5 mini AI
By the triangle inequality, AC is greater than |15 − 25| = 10 and less than 15 + 25 = 40, so 10 < AC < 40.

If Pete goes A → B → C he walks 15 + 25 = 40 yards.

Thus AC is more than 10 yards.

The savings w = (AB + BC) − AC = 40 − AC, so since AC > 10 we have w < 40 − 10 = 30.