SOLUTION: Using the Pythagorean Theorem and a quadratic equation to find side lengths of a right triangle The shorter leg of a right triangle is 9ft shorter than the longer leg. The hypoten

Question 1196615: Using the Pythagorean Theorem and a quadratic equation to find side lengths of a right triangle
The shorter leg of a right triangle is 9ft shorter than the longer leg. The hypotenuse is 9ft longer than the longer leg. Find the side lengths of the triangle.
Short Leg - x-9
Longer Leg x
Hypotenuse x+9
The pythagorean theorem
x^2 + (x-9)^2 = (x+9)^2
And for some reason, I haven't forgotten to factor because my numbers aren't working out.
I need to find what x = so I can figure out the side of each leg of the triangle.
Thank you,
Hannah
Answer by ewatrrr(24785) (Show Source): You can put this solution on YOUR website!


Hi
Good work setting it up:
x^2 + (x-9)^2 = (x+9)^2
Need to Simplify this:
x^2 + x^2 -18x + 81 = x^2 + 18x + 81 
x^2 - 36x = 0            
x(x-36) = 0      |x=0  not appropriate to this problem
x = 36ft    
Side lengths of Triangle are: 27ft, 36ft , 45ft
checking our work Using the Pythagorean Theorem
 27^2 + 36^2 = 2025 = 45^2   Checks
Wish You the Best in your Studies.

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