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Ratio Between the Areas of Two Polygons

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January 12, 2009
ratiogeometrytrigonometry

Problem Statement

In ABC ABC we have AB \equal{} 25, BC \equal{} 39, and AC \equal{} 42. Points D D and E E are on AB AB and AC AC respectively, with AD \equal{} 19 and AE \equal{} 14. What is the ratio of the area of triangle ADE ADE to the area of quadrilateral BCED BCED? <spanclass=′latex−bold′>(A)</span> 2661521<spanclass=′latex−bold′>(B)</span> 1975<spanclass=′latex−bold′>(C)</span> 13<spanclass=′latex−bold′>(D)</span> 1956<spanclass=′latex−bold′>(E)</span> 1 <span class='latex-bold'>(A)</span>\ \frac{266}{1521}\qquad <span class='latex-bold'>(B)</span>\ \frac{19}{75}\qquad <span class='latex-bold'>(C)</span>\ \frac{1}{3}\qquad <span class='latex-bold'>(D)</span>\ \frac{19}{56}\qquad <span class='latex-bold'>(E)</span>\ 1
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