Question

A rectangle field is half as wide as it is long and is completely enclosed by $x$ meter of fencing. What is the area of the field?

• A. $\frac{x^2}{2}{m}^2$
• B. $2x^2{m}^2$
• C. $\frac{2x^2}{9}{m}^2$
• D. $\frac{x^2}{18}{m}^2$

Answer 1

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

Let the breadth of the rectangular field b a Then its length = $2a$ m
Given, $2(2a+a)=x\Rightarrow 6a=\Rightarrow a=\frac{x}{6}m$
$\therefore$ Length = 2a= $2a=2\times \frac{x}{6}=\frac{x}{3}m$
$\therefore$ Area of the rectangular field = $\frac{x}{3}\times \frac{x}{6}=\frac{x^2}{18}{m}^2$