MathDB

16

Part of 2017 AMC 8

Problems(1)

Equal Perimeters

Source: 2017 AMC 8 #16

11/22/2017
In the figure below, choose point DD on BC‾\overline{BC} so that △ACD\triangle ACD and △ABD\triangle ABD have equal perimeters. What is the area of △ABD\triangle ABD? [asy]draw((0,0)--(4,0)--(0,3)--(0,0)); label("AA", (0,0), SW); label("BB", (4,0), ESE); label("CC", (0, 3), N); label("33", (0, 1.5), W); label("44", (2, 0), S); label("55", (2, 1.5), NE);[/asy] <spanclass=′latex−bold′>(A)</span>34<spanclass=′latex−bold′>(B)</span>32<spanclass=′latex−bold′>(C)</span>2<spanclass=′latex−bold′>(D)</span>125<spanclass=′latex−bold′>(E)</span>52<span class='latex-bold'>(A) </span>\frac{3}{4}\qquad<span class='latex-bold'>(B) </span>\frac{3}{2}\qquad<span class='latex-bold'>(C) </span>2\qquad<span class='latex-bold'>(D) </span>\frac{12}{5}\qquad<span class='latex-bold'>(E) </span>\frac{5}{2}