SOLUTION: The hypotenuse of a right triangle is twice as long as one of the legs and 4 inches longer than the other. What are the lengths of the sides of the triangle?

Algebra ->  Triangles -> SOLUTION: The hypotenuse of a right triangle is twice as long as one of the legs and 4 inches longer than the other. What are the lengths of the sides of the triangle?      Log On


   

Question 212968: The hypotenuse of a right triangle is twice as long as one of the legs and 4 inches longer than the other. What are the lengths of the sides of the triangle?
Answer by vleith(2983) About Me  (Show Source):
You can put this solution on YOUR website!
Let h be the length of the hypotenuse. Then one side is h/2 and the third side is h-4.
Since it is a right triangle, you know that
h%5E2+=+%28h%2F2%29%5E2+%2B+%28h-4%29%5E2
h%5E2+=+h%5E2%2F4+%2B+h%5E2+-8h+%2B+16
0+=+h%5E2%2F4+-+8h+%2B+16
0+=+h%5E2+-+32h+%2B+64
Use the quadratic equation to solve
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-32x%2B64+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-32%29%5E2-4%2A1%2A64=768.

Discriminant d=768 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--32%2B-sqrt%28+768+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-32%29%2Bsqrt%28+768+%29%29%2F2%5C1+=+29.856406460551
x%5B2%5D+=+%28-%28-32%29-sqrt%28+768+%29%29%2F2%5C1+=+2.14359353944898

Quadratic expression 1x%5E2%2B-32x%2B64 can be factored:
1x%5E2%2B-32x%2B64+=+1%28x-29.856406460551%29%2A%28x-2.14359353944898%29
Again, the answer is: 29.856406460551, 2.14359353944898. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-32%2Ax%2B64+%29


Since one of the answer is too short to make that number -4 positive, the hypotenuse is ~29.85