Question 148013: One side of a rectangular stage is 2 meters longer than the other.If the diagonal is 10 meters, then what are the lenghths of the sides?
Found 2 solutions by nerdybill, Electrified_Levi:
Answer by nerdybill(7384)   (Show Source):
You can put this solution on YOUR website! One side of a rectangular stage is 2 meters longer than the other.If the diagonal is 10 meters, then what are the lenghths of the sides?
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Let W=width of rectangular stage
W+2 = length of rectangular stage
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Now, since the we have a "right angle" at the corner of the rectangular stage, we can apply Pythagorean theorem:
W^2 + (W+2)^2 = 10^2
W^2 + W^2 + 4W + 4 = 100
2W^2 + 4W - 96 = 0
dividing through by 2:
W^2 + 2W - 48 = 0
factoring:
(W-6)(W+8) = 0
The two solutions are {6, -8}
We can toss out the negative solution since that does not make sense.
Therefore we have:
W= 6 meters (width)
W+2 = 6+2 = 8 meters (length)
Answer by Electrified_Levi(103)  (Show Source):
You can put this solution on YOUR website! Hi, Hope I can help
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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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First you will need to draw a rectangle, with a line in the middle, going from one corner to the other
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We can look and see that it makes two triangles, they are both right triangles.
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We can use the Pythagorean theorem,
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The shorter side is "x", the longer side is two more than the shorter,or (x + 2)
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We can replace "a" and "b" in the Pythagorean theorem, "a" and "b" are the sides
, "c" is the hypotenuse, or diagonal
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We can now solve it even more
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We can divide everything by "2"
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We will move the 50 over to the left side
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We can factor this quadratic equation to  ( (-6) + 8 = 2 )
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We can now solve for "x", taking one factor at a time
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The next factor
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x can be either (-8), or 6
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Our "x" is = 6 meters ( measurements can't be negative)
The shorter side was "x" or 6 meters, our longer side is (x+2) or 8 meters
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You can check by replacing "a" and "b" in the Pythagorean theorem
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Shorter Side = 6 meters
Longer Side = 8 meters
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Hope I helped, Levi
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