Answer:
Step-by-step explanation:
You want the lengths of the two longer sides of a right triangle that differ by 1 mile, given the short side is 13 miles.
Long sides
Let x represent the longer leg of the triangle. By the Pythagorean theorem, we have ...
13² + x² = (x +1)²
169 +x² = x² +2x +1
168 = 2x
84 = x
The missing sides are 84 miles and 85 miles in length.
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Additional comment
As you can see here, when the longer sides differ by 1, their sum is the square of the shorter side.
