The hypotenuse of a right triangle is 5 inches, and the longer leg of the right triangle is 1 inch longer than the shorter leg. Write an equation you could use to find the length of the short leg.

Answer 1

Let x = the shorter leg. Then the longer leg = x + 1.

Using the Pythagorean Theorem you get:

x² + ( x+ 1 )² = 5^{2. *****.} this is the answer to the question.

The following is how you would find x.

x^{2 +} x² + 2x + 1 = 25. ( foil out (x + 1)² )

2x² + 2x - 24 = 0. ( combine like terms and bring everything to one side)

x² + x - 12 = 0 ( divide both sides by 2)

( x + 4 ) ( x - 3 ) = 0. ( factor )

x = -4 or x = 3

Since you can not have a negative length for a side, the answer has to be x = 3