Question 181511
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,
x<sup>2</sup>+(x+2)<sup>2</sup>=10<sup>2</sup>
x<sup>2</sup>+(x<sup>2</sup>+4x+40)=100
2x<sup>2</sup>+4x+40=100
x<sup>2</sup>+2x+20=50
x<sup>2</sup>+2x-30=0
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Using the quadratic formula,
{{{x=(-2+-sqrt(2^2-4(1)(-30)))/2(1)=(-2+-sqrt(4+120))/2=(-2+-sqrt(124))/2=(-2+-2sqrt(31))/2=-1+-sqrt(31)}}}
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Initially we had two values for x. However, {{{-1-sqrt(31)}}} is invalid since it will yield a negative value which is impossible for there are no negative lengths.
Thus, x={{{-1+sqrt(31)}}} m, x+2={{{1+sqrt(31)}}} m. Theses values represent the sides of the rectangle.
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HyperBrain!
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