SOLUTION: I need your help to solve this problem and also what are the steps to solve this problem.
The length of a hypotenuse of a right triangle is 2 feet more than the longer leg. The le
Algebra ->
Quadratic Equations and Parabolas
-> SOLUTION: I need your help to solve this problem and also what are the steps to solve this problem.
The length of a hypotenuse of a right triangle is 2 feet more than the longer leg. The le
Log On
Question 38560: I need your help to solve this problem and also what are the steps to solve this problem.
The length of a hypotenuse of a right triangle is 2 feet more than the longer leg. The length of the longer leg is 7 feet more than the lenth of the shorter leg. Find the number of feet in length of each side of the right triangle.
You can put this solution on YOUR website! For every right triangle, a^2 + b^2 = c^2...
Let x = the length of the shorter leg.
Thus x + 7 is the longer leg and
x + 9 is the length of the hypotenuse...
So substituting into the Pythagorean Theorem, we have
x^2 + (x + 7)^2 = (x + 9)^2
x^2 + (x^2 + 14x + 49) = x^2 + 18x + 81
now collect like terms and solve for x
2x^2 + 14x + 49 = x^2 + 18x + 81
x^2 - 4x - 32 = 0
(x - 8)(x + 4) = 0
x = 8 and x = -4
but distances cannot be negative, so
x = 8
The other sides must be 15 and 17.
