Skip to main content

2016 AMC 12B Problem 9

Problem 9 of 25EasierAlgebraGeometryCounting & Probability

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?

Answer choices

Show solution

Solution

Let the shorter side have xx posts, so the longer side has 2x.2x. Counting all posts and subtracting the four corners counted twice, 2x+2(2x)−4=20,2x+2(2x)-4=20, giving x=4.x=4. The shorter side has 44 posts, or (4−1)⋅4=12(4-1)\cdot4=12 yards, and the longer side has 88 posts, or (8−1)⋅4=28(8-1)\cdot4=28 yards. The area is 12⋅28=336.12\cdot28=336. Thus, the correct answer is B.

More practice

Concepts: fencepost counting · system of equations · rectangle · perimeter

Problem text and solution from the LIVE past-contest archive. See also the AoPS wiki page for community solutions.