MathDB
Perimeter of a Dissected Rectangle

Source:

January 18, 2009
geometryperimeterrectangle

Problem Statement

A rectangle with perimeter 176 176 is divided into five congruent rectangles as shown in the diagram. What is the perimeter of one of the five congruent rectangles? [asy]defaultpen(linewidth(.8pt)); draw(origin--(0,3)--(4,3)--(4,0)--cycle); draw((0,1)--(4,1)); draw((2,0)--midpoint((0,1)--(4,1))); real r = 4/3; draw((r,3)--foot((r,3),(0,1),(4,1))); draw((2r,3)--foot((2r,3),(0,1),(4,1)));[/asy]<spanclass=latexbold>(A)</span> 35.2<spanclass=latexbold>(B)</span> 76<spanclass=latexbold>(C)</span> 80<spanclass=latexbold>(D)</span> 84<spanclass=latexbold>(E)</span> 86 <span class='latex-bold'>(A)</span>\ 35.2\qquad <span class='latex-bold'>(B)</span>\ 76\qquad <span class='latex-bold'>(C)</span>\ 80\qquad <span class='latex-bold'>(D)</span>\ 84\qquad <span class='latex-bold'>(E)</span>\ 86