Question 181511: 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?
Found 2 solutions by HyperBrain, ikleyn:
Answer by HyperBrain(694)   (Show Source):
You can put this solution on YOUR website! A rectangle is a parallelogram that has four right angles [rect-angle]
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Therefore, if we draw one diagonal, we will have two right triangles which, of course, satisfy the Pythagorean theorem.
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Let x=width
. x+2=length
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The diagonal of length 10 acts as the hypotenuse while x and x+2 are the legs. Using the Pythagorean theorem,
x2+(x+2)2=102
x2+(x2+4x+40)=100
2x2+4x+40=100
x2+2x+20=50
x2+2x-30=0
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Using the quadratic formula,
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Initially we had two values for x. However,  is invalid since it will yield a negative value which is impossible for there are no negative lengths.
Thus, x= m, x+2= m. Theses values represent the sides of the rectangle.
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Answer by ikleyn(53937)  (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 lengths of the sides?
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The solution and the answer in the post by @HyperBrain both are incorrect due to arithmetic error.
See my correct solution below.
Let x = width
. . x+2 = length
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The diagonal of length 10 acts as the hypotenuse while x and x+2 are the legs. Using the Pythagorean theorem,
x2+(x+2)^2 = 10^2
x^2 + x^2 + 4x + 4 = 100
2x^2 + 4x - 96 = 0
x^2 + 2x - 48 = 0
(x+8)*(x-6) = 0
Use the positive root x = 6.
The sides are 6 meters and 8 meters. ANSWER
Solved correctly.
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