SOLUTION: Question 11 The longer leg of a right triangle is 4m longer than the shorter leg. The hypotenuse is 8m longer than the shorter leg. Find the side lengths of the triangle.

Algebra ->  Linear-equations -> SOLUTION: Question 11 The longer leg of a right triangle is 4m longer than the shorter leg. The hypotenuse is 8m longer than the shorter leg. Find the side lengths of the triangle.       Log On


   

Question 1112581: Question 11
The longer leg of a right triangle is 4m longer than the shorter leg.
The hypotenuse is 8m longer than the shorter leg. Find the side lengths of the triangle.

Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
x%5E2 + %28x%2B4%29%5E2 = %28x%2B8%29%5E2.


x^2 + x^2 + 8x + 16 = x^2 + 16x + 64.


x2 - 8x - 48 = 0


(x-12)*(x+4) = 0


The only positive root x= 12 works.


Check.   12^2 + 16^2 = 144 + 256 = 400 = 20^2.


Answer.  (12,16,20), classic (3,4,5)-right angled triangle.