Question

Runners in a long distance race start out going 5 kilometers south and then head west for the remainder of the race. The finish line is 13 kilometers from the starting line. How far did the runners travel?

Answer 1

You may recognize the numbers as belonging to the (5, 12, 13) Pythagorean triple. The runners traveled 12 km west after traveling 5 km south. Their total distance was ...
5 km +12 km = 17 km

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By the Pythagorean theorem, ...
(straight-line distance)² = (distance south)² +(distance west)²
In km, this is
13² = 5² +(distance west)²
169 -25 = (distance west)²
√144 = 12 = distance west