Dissected Rectangle
Source:
January 5, 2007
geometryrectangleperimeteralgorithmgreatest common divisornumber theoryrelatively prime
Problem Statement
The diagram shows a rectangle that has been dissected into nine non-overlapping squares. Given that the width and the height of the rectangle are relatively prime positive integers, find the perimeter of the rectangle.[asy]
defaultpen(linewidth(0.7));
draw((0,0)--(69,0)--(69,61)--(0,61)--(0,0));draw((36,0)--(36,36)--(0,36));
draw((36,33)--(69,33));draw((41,33)--(41,61));draw((25,36)--(25,61));
draw((34,36)--(34,45)--(25,45));
draw((36,36)--(36,38)--(34,38));
draw((36,38)--(41,38));
draw((34,45)--(41,45));[/asy]