help! me! please!

Question

Find the length of the shorter leg of a right triangle if the longer leg is 13 feet more than the shorter leg and the hypotenuse is 13 feet less than twice the shorter leg.

Answer 1

Let x = short leg, then long leg = (x+13) and the hypotenuse = (2x-13).

 

a² + b² = c²

 

x² + (x+13)² = (2x-13)²

 

x² + x² + 26x + 169 = 4x² - 52x + 169

 

2x² - 78x = 0

 

x² - 39x = 0

 

x (x -39)=0  x is 0 (which is impossible) or x = 39