Problem
1964 AHSME Problem 33
P is a point interior to rectangle ABCD and such that PA=3 inches, PD=4 inches, and PC=5 inches. Then PB, in inches, equals:
\textbf{(A) }2\sqrt{3}\qquad \textbf{(B) }3\sqrt{2}\qquad \textbf{(C) }3\sqrt{3}\qquad \textbf{(D) }4\sqrt{2}\qquad \textbf{(E) }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("$A$",(0,0),dir(-135)); label("$B$",(6.5,0),dir(-45)); label("$C$",(6.5,4.5),dir(45)); label("$D$",(0,4.5),dir(135)); label("$P$",(2.5,1.5),dir(-90)); label("$3$",(1.25,0.75),dir(120)); label("$4$",(1.25,3),dir(35)); label("$5$",(4.5,3),dir(120)); //Credit to bobthesmartypants for the diagram[/asy]](/static/aops/89fbb437f173f73096e2c066c53c3e92d777872c.png)
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