SOLUTION: Rectangular stage. One side of a rectangular stage is 2 meters longer than the other. If the diagonal is 10 meters, then what are the lengths of the sides?

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Rectangular stage. One side of a rectangular stage is 2 meters longer than the other. If the diagonal is 10 meters, then what are the lengths of the sides?      Log On


   

Question 146944: Rectangular stage. One side of a rectangular stage is 2 meters longer than the other. If the diagonal is 10 meters, then what are the lengths of the sides?
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Rectangular stage. One side of a rectangular stage is 2 meters longer than the other. If the diagonal is 10 meters, then what are the lengths of the sides?
--------------
L%5E2+%2B+%28L%2B2%29%5E2+=+10%5E2 (Pythagoras)
L%5E2+%2B+L%5E2+%2B+4L+%2B+4+=+100
2L%5E2+%2B+4L+%2B+4+=+100
L%5E2+%2B+2L+-+48+=+0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B2x%2B-48+=+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=%282%29%5E2-4%2A1%2A-48=196.

Discriminant d=196 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-2%2B-sqrt%28+196+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%282%29%2Bsqrt%28+196+%29%29%2F2%5C1+=+6
x%5B2%5D+=+%28-%282%29-sqrt%28+196+%29%29%2F2%5C1+=+-8

Quadratic expression 1x%5E2%2B2x%2B-48 can be factored:
1x%5E2%2B2x%2B-48+=+%28x-6%29%2A%28x--8%29
Again, the answer is: 6, -8. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B2%2Ax%2B-48+%29

Discard the negative length, so L = 6, and the longer side is 8.
6, 8, 10 is a right triangle.