Question

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

Answer 1

Answer:

Step-by-step explanation:

Let l and w be the length and width (breadth) of the rectangular field respectively

Given

w = $\frac{l}{2}$

Given the perimeter of the field = x meters.

That is x meters = 2( l+w)

$x = 2( l+\frac{l}{2} )\\\\x = 2(\frac{2l+l}{2})$

$x= 3l\\\\l = \frac{x}{3}$

If $l = \frac{x}{3}$, then w =

$\frac{1}{2} *\frac{x}{3} \\\\= \frac{x}{6}$

Area of the field = l*w

= $\frac{x}{3} *\frac{x}{6} \\\\=\frac{x^{2}}{18}$

Therefore the area of the field in terms of x is $\frac{x^{2} }{18}$$m^{2}$