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trapezoid inequality

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April 28, 2009
geometrytrapezoidinequalitiestrigonometrytriangle inequality

Problem Statement

In trapezoid ABCD ABCD, AB∥CD AB \parallel CD, ∠CAB<90∘ \angle CAB < 90^\circ, AB \equal{} 5, CD \equal{} 3, AC \equal{} 15. What are the sum of different integer values of possible BD BD?
<spanclass=′latex−bold′>(A)</span> 101<spanclass=′latex−bold′>(B)</span> 108<spanclass=′latex−bold′>(C)</span> 115<spanclass=′latex−bold′>(D)</span> 125<spanclass=′latex−bold′>(E)</span> None<span class='latex-bold'>(A)</span>\ 101 \qquad<span class='latex-bold'>(B)</span>\ 108 \qquad<span class='latex-bold'>(C)</span>\ 115 \qquad<span class='latex-bold'>(D)</span>\ 125 \qquad<span class='latex-bold'>(E)</span>\ \text{None}
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