2010 Geometry #2
Source:
January 2, 2024
geometry
Problem Statement
A rectangular piece of paper is folded along its diagonal (as depicted below) to form a non-convex pentagon that has an area of of the area of the original rectangle. Find the ratio of the longer side of the rectangle to the shorter side of the rectangle.
[asy]
size(150);
pair A = (-5,0);
pair B = (5,0);
pair C = (-3,4);
pair D = (3,4);
pair E = intersectionpoint(B--C,A--D);
draw(A--B--D--cycle);
draw(A--C);
draw(C--E);
draw(E--B,dashed);
markscalefactor=0.06;
draw(rightanglemark(A,C,B));
[/asy]