ratio of the hypotenuse over perimeter
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April 23, 2009
ratiogeometryperimetertrigonometry
Problem Statement
In a right triangle, ratio of the hypotenuse over perimeter of the triangle determines an interval on real numbers. Find the midpoint of this interval?(A)\ \frac{2\sqrt{2} \plus{}1}{4} \qquad(B)\ \frac{\sqrt{2} \plus{}1}{2} \qquad(C)\ \frac{2\sqrt{2} \minus{}1}{4} \\ \qquad(D)\ \sqrt{2} \minus{}1 \qquad(E)\ \frac{\sqrt{2} \minus{}1}{2}