Problem:
Carl decided to fence in his rectangular garden. He bought 20 fence posts, placed one on each of the four corners, and spaced out the rest evenly along the edges of the garden, leaving exactly 4 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:
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Solution:
Let be the number of posts along the shorter side; then there are posts along the longer side. When counting the number of posts on all the sides of the garden, each corner post is counted twice, so . Solving this equation gives . Thus the dimensions of the rectangle are yards by yards. The requested area is given by the product of these dimensions, square yards.
The problems on this page are the property of the MAA's American Mathematics Competitions