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?

Algebra ->  Polynomials-and-rational-expressions -> 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?      Log On


   

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) About Me  (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) About Me  (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
L=W%2B2


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


L%5E2%2BW%5E2=10%5E2


%28W%2B2%29%5E2%2BW%5E2=10%5E2 Plug in L=W%2B2


W%5E2%2B4W%2B4%2BW%5E2=10%5E2 Foil


W%5E2%2B4W%2B4%2BW%5E2=100 Square 10 to get 100



W%5E2%2B4W%2B4%2BW%5E2-100=0 Subtract 100 from both sides


2W%5E2%2B4W-96=0 Combine like terms


2%28w%2B8%29%28w-6%29=0 Factor the left side



Now set each factor equal to zero:
w%2B8=0 or w-6=0

w=-8 or w=6 Now solve for w in each case


So our possible answers are
w=-8 or w=6


However, since a negative width doesn't make sense, our only solution is w=6



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

L=W%2B2 Start with the given equation


L=6%2B2 Plug in W=6


L=8 Add

So the length is 8 meters