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

Question 120314: One side of a rectangular stage is 2meters longer than the other. If the diagonal is 10 meters, then what are the lengths of the sides?
Found 2 solutions by checkley71, jim_thompson5910:
Answer by checkley71(8403) (Show Source): You can put this solution on YOUR website!
X^2+(X+2)^2=10^2
X^2+X^2+4X+4=100
2X^2+4X+4-100=0
2X^2+4X-96=0
2(X^2+2X-48)=0
2(X+8)(X-6)=0
X+8=0
X=-8 ANSWER.
X-6=0
X=6 ANSWER.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Let L=length , W=width

Since one side (say the length) "is 2meters longer than the other" then this means

Now using Pythagoreans theorem, we can set up a relationship between the length, width, and the diagonal:

Plug in

Foil

Square 10 to get 100

Subtract 100 from both sides

Combine like terms

Factor the left side

Now set each factor equal to zero:
or

or Now solve for w in each case

So our possible answers are
or

However, since a negative width doesn't make sense, our only solution is

So the width is 6 meters. Now let's find the length

Start with the given equation

Plug in

Add

So the length is 8 meters