If you remember the a2 + b2 = c2 rule from maths class, that’s what’ll help you solve this problem. This rule states that if you have a triangle, the sum of the squares of the two shorter sides equals the square of the longest side. And in this problem, the walkers’ paths form parts of triangles. You may want a pencil and paper to “draw out” this problem and visualize the triangles.
Draw two lines labelled “three feet” for the distance they walk away from each other. Then draw two lines labelled “four feet,” going in opposite directions, for the distance they walked after their left turns. Now draw a line connecting the points at the ends of those lines (representing where the people are now). This line represents the distance you’re trying to figure out.
Now, you’ve got two triangles touching at the corners. Two sides of each are 3 feet and 4 feet (the distances each person walked). The unknown sides represent two halves of the distance you’re trying to find. So break out that Pythagorean Theorem: Three is a, 4 is b. 32 + 42 = 9 + 16 = 25 = c2. Take the square root of 25 and you get 5, which is the longest side of these mini-triangles. Five feet is half of the distance between the people. Five times two is ten! Here’s another three-sided puzzler: try to figure out how many triangles are in this image.