Question

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

• A. $\frac{x^2}{2}$
• B. $2x^2$
• C. $\frac{2x^2}{9}$
• D. $\frac{x^2}{18}$
• E. none of these

Answer 1

The correct option is D $\frac{x^2}{18}$

Let the dimension of the field be $w$ and $2w$

since length of fencing = perimeter
Then $2(w+2w)=x$

$6w=x$

$w=\frac{x}{6}$

and $2w=\frac{x}{3}$.
$\therefore Area=w\cdot 2w=\frac{x^2}{18}$.