The hypotenuse of right triangle

Question

the hypotenuse of a right triangle is 3 meters longer than twice the length of the shorter leg. The longer leg is 12 meters. Find the length of the shorter leg.

Answer 1

Let x = length of the shorter leg

 

Then 2x+3 = length of the hypotenuse

 

By the Pythagorean Theorem, x² + 12² = (2x+3)²

 

                                            x² + 144 = 4x² + 12x + 9

 

                                            3x² + 12x - 135 = 0

 

                                              x² + 4x - 45 = 0

 

                                              (x+9)(x-5) = 0

 

                                             x = -9 or 5

 

Since x can't be negative, x = 5 meters