Question

1.For this problem, 200 meters of fencing will all be used to place fence on all four sides of the rectangle. Your task is to write the area that can be enclosed as a function of the width, w, of the rectangle.

Area equation:


What is the domain for this function (what values do you expect the width to fall between)?

Answer 1

Explanation:

Given that:

the perimeter of the fencing (rectangle) = 200

Let recall that the area equation of a rectangle = L × w

The perimeter now = 2(L + w)

The perimeter = 2L + 2w

∴

200 = 2L +2w

Dividing both sides by 2

100 = L + w

Making Length L the subject; we have:

- L = -100 + w

L = 100 - w

Thus;

A(w) = (100 - w) w

and the domain of the function is (0,100)