MathDB
Carl The Garden Fencer

Source: Problem #11 2016 AMC 10B and #9 AMC 12

February 21, 2016
AMCAMC 102016 AMC 10BAMC 10 B

Problem Statement

Carl decided to fence in his rectangular garden. He bought 2020 fence posts, placed one on each of the four corners, and spaced out the rest evenly along the edges of the garden, leaving exactly 44 yards between neighboring posts. The longer side of his garden, including the corners, has twice as many posts as the shorter side, including the corners. What is the area, in square yards, of Carl’s garden?
<spanclass=latexbold>(A)</span> 256<spanclass=latexbold>(B)</span> 336<spanclass=latexbold>(C)</span> 384<spanclass=latexbold>(D)</span> 448<spanclass=latexbold>(E)</span> 512<span class='latex-bold'>(A)</span>\ 256\qquad<span class='latex-bold'>(B)</span>\ 336\qquad<span class='latex-bold'>(C)</span>\ 384\qquad<span class='latex-bold'>(D)</span>\ 448\qquad<span class='latex-bold'>(E)</span>\ 512