Rectangle in a Triangle
Source:
June 8, 2009
geometryrectangleperimeter
Problem Statement
In right triangle , BC \equal{} 5, AC \equal{} 12, and AM \equal{} x; , ; is on . If y \equal{} MN \plus{} NP, one-half the perimeter of rectangle , then:
[asy]defaultpen(linewidth(.8pt));
unitsize(2cm);
pair A = origin;
pair M = (1,0);
pair C = (2,0);
pair P = (2,0.5);
pair B = (2,1);
pair Q = (1,0.5);draw(A--B--C--cycle);
draw(M--Q--P);label("",A,SW);
label("",M,S);
label("",C,SE);
label("",P,E);
label("",B,NE);
label("",Q,NW);[/asy] (A)\ y \equal{} \frac {1}{2}(5 \plus{} 12) \qquad (B)\ y \equal{} \frac {5x}{12} \plus{} \frac {12}{5}\qquad (C)\ y \equal{} \frac {144 \minus{} 7x}{12}\qquad
(D)\ y \equal{} 12\qquad \qquad \,\, (E)\ y \equal{} \frac {5x}{12} \plus{} 6