The longer leg of a right triangle is 2 inches more than twice the length of the shorter leg The hpotenuse is 2 inches less than 3 times the length of the shorter leg Find the length of the hpotenuse

Answer 1

Draw a picture.

Let "s" be the short leg. Then the Long Leg is 2s + 2. The hypotenuse is 3s - 2.

Now use the Pythagorean Theorem a² + b² = c². (short leg)² + (long leg)² = (hypotenuse)² or:

s² + (2s + 2)² = (3s - 2)²

Multiply this out using the FOIL method to get:

s² + 4s² + 8s + 4 = 9s² - 12s + 4

To solve a quadratic, move everything to one side, combine like terms, (set the quadratic equal to zero), then factor and set each piece equal to zero.

4s² - 20s = 0

4s(s - 5) = 0

or 4s = 0 and (s - 5) = 0 which means there are two solutions, s = 0 and s = 5 but if s = 0, it's not a triangle, so that solution does not make sense in this problem. So s = 5.

To find the hypotenuse, plug in s = 5 to the equation for the hypotenuse (hyp = 3s - 2)