MathDB
Find the missing length, PB

Source: 1964 AHSME Problem 33

March 19, 2014
geometryrectangleAMC

Problem Statement

PP is a point interior to rectangle ABCDABCD and such that PA=3PA=3 inches, PD=4PD=4 inches, and PC=5PC=5 inches. Then PBPB, in inches, equals:
<spanclass=latexbold>(A)</span>23<spanclass=latexbold>(B)</span>32<spanclass=latexbold>(C)</span>33<spanclass=latexbold>(D)</span>42<spanclass=latexbold>(E)</span>2<span class='latex-bold'>(A) </span>2\sqrt{3}\qquad<span class='latex-bold'>(B) </span>3\sqrt{2}\qquad<span class='latex-bold'>(C) </span>3\sqrt{3}\qquad<span class='latex-bold'>(D) </span>4\sqrt{2}\qquad <span class='latex-bold'>(E) </span>2
[asy] draw((0,0)--(6.5,0)--(6.5,4.5)--(0,4.5)--cycle); draw((2.5,1.5)--(0,0)); draw((2.5,1.5)--(0,4.5)); draw((2.5,1.5)--(6.5,4.5)); draw((2.5,1.5)--(6.5,0),linetype("8 8")); label("AA",(0,0),dir(-135)); label("BB",(6.5,0),dir(-45)); label("CC",(6.5,4.5),dir(45)); label("DD",(0,4.5),dir(135)); label("PP",(2.5,1.5),dir(-90)); label("33",(1.25,0.75),dir(120)); label("44",(1.25,3),dir(35)); label("55",(4.5,3),dir(120)); //Credit to bobthesmartypants for the diagram [/asy]