SOLUTION: 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?

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?
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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