Suppose that one leg of a right triangle is 7 feet shorter than the other leg. The hypotenuse is 2 feet longer than the longer leg. Find the lengths of all three sides of the right triangle.

Answer 1

Draw a figure.

One leg is x, one is x+7 and the hypotenuse is x+9.

Theorem of Pythagoras: x² + x² + 14x + 49 = x² +18x + 81

x² - 4x -32=0

This factors easily into one extraneous root and x = 8. You find the rest!