SOLUTION: 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.

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Question 141921: 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 jojo14344(1513) About Me  (Show Source):
You can put this solution on YOUR website!
We use pythagorean theorem.
smaller side= "x"= a
longer side= "x+2"= b
diagonal side=10m = c
So,
c^2=a^2 + b^2
10^2= x^2 + (x+2)^2
100= x^2 + x^2 + 4x + 4
2x^2 + 4x - 96 =0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 2x%5E2%2B4x%2B-96+=+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=%284%29%5E2-4%2A2%2A-96=784.

Discriminant d=784 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-4%2B-sqrt%28+784+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%284%29%2Bsqrt%28+784+%29%29%2F2%5C2+=+6
x%5B2%5D+=+%28-%284%29-sqrt%28+784+%29%29%2F2%5C2+=+-8

Quadratic expression 2x%5E2%2B4x%2B-96 can be factored:
2x%5E2%2B4x%2B-96+=+%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+2%2Ax%5E2%2B4%2Ax%2B-96+%29

we use x=6 , smaller side
The other, X+2=6+2=8, longer side
thank you,
Jojo