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?

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Question 200792This question is from textbook Elementary and Intermediate Algebra
: 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? This question is from textbook Elementary and Intermediate Algebra

Found 2 solutions by stanbon, rfer:
Answer by stanbon(75887) (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?
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Draw a rectangle.
label a short side as "x".
label a long side as "x+2"
label a diagonal as 10 meters
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See the right triangle with the diagonal as its hypotenuse?
Use Pytagoras:
x^2 + (x+2)^2 = 10^2
2x^2 + 4x - 96 = 0
x^2 + 2x - 48 = 0
Factor:
(x+8)(x-6) = 0
Positive solution:
x = 6 (shorter side)
x+2 = 8 (longer side)
===========================
Cheers,
Stan H.

Answer by rfer(16322) (Show Source):
You can put this solution on YOUR website!
x^2+(x+2)^2=(10)^2
2x^2+4x-96=0
a=2 b=4 c=-96
b^2-4(2)(-96)=768
Sq root of 768=28
x=(-4+or-28)/4
x=(-4+28)/4=6
w=6
l=w+2=8