MathDB
Three Congruent Rectangles

Source: 2019 AMC 8 #2

November 22, 2019
AMC 8geometryrectangle

Problem Statement

Three identical rectangles are put together to form rectangle ABCDABCD, as shown in the figure below. Given that the length of the shorter side of each of the smaller rectangles 55 feet, what is the area in square feet of rectangle ABCDABCD? [asy]draw((0,0)--(0,10)--(15,10)--(15,0)--(0,0)); draw((0,5)--(10,5)); draw((10,0)--(10,10)); label("AA",(0,0),SW); label("BB",(15,0),SE); label("CC",(15,10),NE); label("DD",(0,10),NW); dot((0,10)); dot((15,0)); dot((15,10)); dot((0,0)); [/asy] <spanclass=latexbold>(A)</span>45<spanclass=latexbold>(B)</span>75<spanclass=latexbold>(C)</span>100<spanclass=latexbold>(D)</span>125<spanclass=latexbold>(E)</span>150<span class='latex-bold'>(A) </span>45\qquad <span class='latex-bold'>(B) </span>75\qquad <span class='latex-bold'>(C) </span>100\qquad <span class='latex-bold'>(D) </span>125\qquad <span class='latex-bold'>(E) </span>150\qquad