MathDB
Three Unit Squares

Source: 2012 AMC10A Problem #15

February 8, 2012
geometryanalytic geometrygraphing linessloperatiosimilar trianglesAMC

Problem Statement

Three unit squares and two line segments connecting two pairs of vertices are shown. What is the area of ABC\triangle ABC?
[asy] size(200); defaultpen(linewidth(.6pt)+fontsize(12pt)); dotfactor=4; draw((0,0)--(0,2)); draw((0,0)--(1,0)); draw((1,0)--(1,2)); draw((0,1)--(2,1)); draw((0,0)--(1,2)); draw((0,2)--(2,1)); draw((0,2)--(2,2)); draw((2,1)--(2,2)); label("AA",(0,2),NW); label("BB",(1,2),N); label("CC",(4/5,1.55),W); dot((0,2)); dot((1,2)); dot((4/5,1.6)); dot((2,1)); dot((0,0)); [/asy]
<spanclass=latexbold>(A)</span> 16<spanclass=latexbold>(B)</span> 15<spanclass=latexbold>(C)</span> 29<spanclass=latexbold>(D)</span> 13<spanclass=latexbold>(E)</span> 24 <span class='latex-bold'>(A)</span>\ \frac{1}{6}\qquad<span class='latex-bold'>(B)</span>\ \frac{1}{5}\qquad<span class='latex-bold'>(C)</span>\ \frac{2}{9}\qquad<span class='latex-bold'>(D)</span>\ \frac{1}{3}\qquad<span class='latex-bold'>(E)</span>\ \frac{\sqrt2}{4}