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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:

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\frac{x^{2}}{2}

2 x^{2}

\frac{{2 x}^{2}}{9}

\frac{x^{2}}{18}

answer is D.

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Detailed Solution

Concept- We’ll use the formula of perimeter of rectangle

2 (l + b)

. We’ll find the area of the rectangle in terms of the given perimeter. Assume the length is

l

then its width must be equal to

\frac{l}{2}

.
Let’s assume the length of yard be

l

and

b = \frac{l}{2}

It is given that the rectangle field is enclosed by

x

yards of fencing which means its perimeter is equal to

x

yards.

Perimeter = 2 (l + b)

Perimeter = 2 (l + \frac{l}{2})

x = 3 l

l = \frac{x}{3}

Now, area of given rectangle field,

Area = l \times b

Area = l \times \frac{l}{2}

Area = \frac{l^{2}}{2}

Putting the value of

l

in above equation,

Area = \frac{{(\frac{x}{3})}^{2}}{2}

Area = \frac{x^{2}}{18}

Hence, option 4 is correct, area of terms in

x

\frac{x^{2}}{18}

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