# 1951 AHSME Problems/Problem 2

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## Problem

A rectangular field is half as wide as it is long and is completely enclosed by $x$ yards of fencing. The area in terms of $x$ is:

$(\mathrm{A})\ \frac{x^2}2 \qquad (\mathrm{B})\ 2x^2 \qquad (\mathrm{C})\ \frac{2x^2}9 \qquad (\mathrm{D})\ \frac{x^2}{18} \qquad (\mathrm{E})\ \frac{x^2}{72}$

## Solution

Let $w$ be the width. Then $l = 2w$, and the perimeter is $x = 2(2w)+2w = 6w \implies w = \frac{x}6$. The area is $wl = w(2w) = 2w^2 = 2\left(\frac{x^2}{36}\right) = \frac{x^2}{18}$, so the answer is $\mathrm{D}$.

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