SOLUTION: The hypotenuse of a right triangle is 25 m long. The length of one leg is 10 m less than twice the other. Find the length of each leg.

Algebra ->  Problems-with-consecutive-odd-even-integers -> SOLUTION: The hypotenuse of a right triangle is 25 m long. The length of one leg is 10 m less than twice the other. Find the length of each leg.      Log On


   

Question 163559This question is from textbook
: The hypotenuse of a right triangle is 25 m long. The length of one leg is 10 m less than twice the other. Find the length of each leg. This question is from textbook

Answer by checkley77(12844) About Me  (Show Source):
You can put this solution on YOUR website!
(2x-10)^2+x^2=25^2
4x^2-40x+100+x^2=625
5x^2-40x+100-625=0
5x^2-40x-525=0
5(x^2-8x-105)=0
5(x-15)(x+7)=0
x-15=0
x=15 for the short side.
2*15-10
30-10=20 for the long side.
Proof:
15^2+20^2=25^2
225+400=625
625=625