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)   (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 (in our case ) has the following solutons:



For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=784 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 6, -8. Here's your graph:

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

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