Question

David has available 2800 yards of fencing and wishes to enclose a rectangular area. Express the area A of the rectangle as a function of the width W of the rectangle.

Answer 1

The area of the rectangular area is (1400w-w²) square yards.

Explanation:

Given that,

David has available 2800 yards of fencing. He wants to enclose a rectangular area.

Assume that, the length and width of the rectangular be l and w respectively.

The perimeter of the rectangular area is

=2(length+ width)

=2(l+w)

So,

2(l+w)= 2800

`\Rightarrow l+w= (2800)/(2)`

`\Rightarrow l+w= 1400`

`\therefore l= 1400-w`

The area of the rectangular area is = length× width

=l×w

=(1400-w) w

=(1400w-w²) square yards.