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.

Explanation:

Step1: Calculate distance from A - B - C

Add distance from A to B and B to C.
$15 + 25=40$

Step2: Apply triangle - inequality

The sum of two sides of a triangle is greater than the third side. So the direct distance from A to C is more than the difference of the other two sides. $25−15 = 10$.

Step3: Calculate maximum savings

The maximum distance saved by taking the direct path is the sum of the two non - direct sides minus the minimum value of the direct side. The sum of A - B and B - C is 40 yards, and the minimum value of A - C is 10 yards. So the maximum savings $w$ is $40−10=30$.

Answer:

How far would Pete walk if he went from A to B to C? 40 yards
The direct distance from A to C is more than 10 yards.
The inequality $w < 30$ represents the distance, $w$, that Pete might save by taking the direct path.