SOLUTION: find the lengthof three sides of the right triangle. x+8,x,x+4

Algebra ->  Triangles -> SOLUTION: find the lengthof three sides of the right triangle. x+8,x,x+4      Log On


   

Question 250744: find the lengthof three sides of the right triangle. x+8,x,x+4
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
If x+8, x and x+4 are the sides of a right triangle then they must fit the equation of the Pythagorean Theorem. We just have to know which side is the hypotenuse so we can put these expressions in the right places.

It shouldn't take long to figure which side is the longest, even though we have no idea what x will turn out to be. Whatever x turns out to be, won't x+8 always be larger than x or x+4? Since x+8 is the largest side it must be the hypotenuse and so its square goes by itself one side of the equation:
%28x%2B8%29%5E2+=+x%5E2+%2B+%28x%2B4%29%5E2
Now we solve this for x. Start by simplifying:
x%5E2+%2B16x+%2B64+=+x%5E2+%2B+x%5E2+%2B+8x+%2B16
x%5E2+%2B+16x+%2B64+=+2x%5E2+%2B8x+%2B16
Since this is a quadratic equation we will get one side equal to zero. Subtracting x%5E2, 16x and 64 from each side we get:
0+=+x%5E2+-8x+-+48
Now we factor (or use the Quadratic Formula). This factors pretty easily:
0+=+%28x-12%29%28x%2B4%29
By the Zero Product Property this product can only be zero is one of the factors is zero. So:
x-12+=+0 or x%2B4+=+0
Solving these we get:
x+=+12 or x+=+-4
Since x represents the length of a side of a triangle, we will reject the negative solution. So x = 12, That makes the other two sides 12+4 = 16 and 12+8 = 20.