Question

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.​

Answer 1

Pete would walk 40 yards if he went from point A to B to C. However, the direct distance from A to C using the Pythagorean theorem is approximately 29.15 yards, and he might save a distance reflected by the inequality w < 40 yards.

Step-by-step explanation:

According to the scenario given, Pete would walk a total distance of 15 yards + 25 yards = 40 yards if he went from A to B to C. However, to find the direct distance from A to C, we need to use the Pythagorean theorem, a2 + b2 = c2, where a and b are the lengths of the legs of the right triangle, and c is the length of the hypotenuse (the straight-line path from A to C).

Let a = 15 yards (distance from A to B), b = 25 yards (distance from B to C), and c = w (the direct distance from A to C). So we have:

152 + 252 = w2
225 + 625 = w2
850 = w2
√850 = w
Approximately 29.15 yards = w

The direct distance from point A to point C is approximately 29.15 yards. If Pete saves distance by walking directly from A to C, the inequality describing this savings could be represented as w < 40 yards.