The shorter leg of a right triangle is 14 feet less than the other leg. Find the length of the two legs if the hypotenuse is 34 feet.

Answer 1

Right triangle, with sides a, b=a-14 and h=34

By Pythagorean rule, h² = 34² = a² + b² = a² + (a-14)² ==> a² + a² - 28a + 196

Simplify to get 1156 = 2a² - 28a + 196

Subtract 1156 from both sides to get 2a² - 28a - 960 = 0

Divide all terms by 2: a² -14a - 480 = 0

Use quadratic equation to find that a = 30 or a = -16.

a = -16 will not work.

Therefore side a = 30 feet long.and side b = 30-14 = 16 feet long.

Check: 30² + 16² = 900+256=1156. SQRT(1156) = 34 feet, the given hypotenuse.