MathDB

Equal Perimeters

Source: 2017 AMC 8 #16

November 22, 2017

Problem Statement

In the figure below, choose point

D

on

\overline{BC}

so that

\triangle ACD

and

\triangle ABD

have equal perimeters. What is the area of

\triangle ABD

? [asy]draw((0,0)--(4,0)--(0,3)--(0,0)); label("

A

", (0,0), SW); label("

B

", (4,0), ESE); label("

C

", (0, 3), N); label("

3

", (0, 1.5), W); label("

4

", (2, 0), S); label("

5

", (2, 1.5), NE);[/asy]

<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}

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