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Source: 2017 AMC 12B #8

February 16, 2017
ratiogeometryrectangle

Problem Statement

The ratio of the short side of a certain rectangle to the long side is equal to the ratio of the long side to the diagonal. What is the square of the ratio of the short side to the long side of this rectangle?
<spanclass=′latex−bold′>(A)</span> 3−12<spanclass=′latex−bold′>(B)</span> 12<spanclass=′latex−bold′>(C)</span> 5−12<spanclass=′latex−bold′>(D)</span> 22<spanclass=′latex−bold′>(E)</span> 6−12<span class='latex-bold'>(A)</span> \text{ } \frac{\sqrt{3}-1}{2} \qquad <span class='latex-bold'>(B)</span> \text{ } \frac{1}{2} \qquad <span class='latex-bold'>(C)</span> \text{ } \frac{\sqrt{5}-1}{2} \qquad <span class='latex-bold'>(D)</span> \text{ } \frac{\sqrt{2}}{2} \qquad <span class='latex-bold'>(E)</span> \text{ } \frac{\sqrt{6}-1}{2}
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