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? \boxed{} yards
the direct distance from a to c is more than \boxed{} yards.
the inequality $w < \boxed{}$ represents the distance, $w$, that pete might save by taking the direct path.

Explanation:

Step1: Calculate A to B to C distance

Add AB and BC: $15 + 25 = 40$

Step2: Find lower bound of AC

Use triangle inequality: $AC > |BC - AB| = |25 - 15| = 10$

Step3: Find upper bound of saved distance

Saved distance $w = 40 - AC$, so $w < 40 - 10 = 30$

Answer:

40
10
30