SOLUTION: The hypotenuse of a right triangle is 9 cm longer than the longer leg. The shorter leg is 23m shorter than the longer leg. Find the length of the longer leg of the triangle.

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: The hypotenuse of a right triangle is 9 cm longer than the longer leg. The shorter leg is 23m shorter than the longer leg. Find the length of the longer leg of the triangle.       Log On


   

Question 1116826: The hypotenuse of a right triangle is 9 cm longer than the longer leg. The shorter leg is 23m shorter than the longer leg. Find the length of the longer leg of the triangle.
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
---
The shorter leg is 23m shorter than the longer leg.
---

y-23, short leg
y, long leg


---
hypotenuse of a right triangle is 9 cm longer than the longer leg.
---

y%2B9, hypotenuse


-------------------------------------------
Find the length of the longer leg of the triangle.
-------------------------------------------

%28y%2B9%29%5E2=y%5E2%2B%28y-23%29%5E2
-
y%5E2%2B18y%2B81=y%5E2%2By%5E2-46y%2B529
18y%2B81=y%5E2-46y%2B529
y%5E2-64y%2B448=0

y=%2864%2B-+48%29%2F2

cross%28y=8%29 or highlight%28y=56%29



-

Also factorable, y%5E2-64y%2B448=%28y-8%29%28y-56%29