I'm stuck with a precalculus work question, can someone help?

Question

A tailor uses 16 ft of lace to trim the edges of a rectangular tablecloth. If the tablecloth is w feet wide, express its area as a function of the width.

Answer 1

the equations are:

2w + 2h = 16

Because you know that the perimeter is 16 ft.

A = hw

Because of course, the area is the product of height (h) and width (w).

From the first equation, with elementary passages, you have:

h = 8 - w

Substitute this in the second:

A = (8-w)w = 8w - w^2

You can choose if you prefer the factored form [ (8-w)w ] which is more elegant, or the developed form [8w - w^2], which is easier to evaluate once you have a certain numerical value of "w". No need to say that they are equivalent.

Answer 2

Assume the 16 ft is all used so the perimeter is 16 ft

Perimeter = 2L + 2W = 16
2L = 16 - 2W
L = 8 - W

Area = LW

A = (8 - W)W = 8W - W^2

Answer 3

let w ft be the length of the tablecloth.
let b ft be the breadth of the tablecloth.

Perimeter of a rectangle
= length + length + breadth + breadth
= 2 (length + breadth)
= 2 (w ft + b ft)

From the question,
2 (w ft + b ft) = 16 ft
w ft + b ft = 8 ft

To express area as a function of the width, express b in terms of w,
b ft = 8-w ft

Hence, sub the equation into the following:
Area of a rectangle
= length * breadth
= w ft * b ft
= w ft * (8-w) ft
= w (8-w) ft^2
= 8w - w^2 ft^2 (optional expansion)

Answer 4

1. Eqn for perimeter:
2W + 2L = 16

2. Solve for Length:
L = 8-W

3. Eqn for area:
Area = L*W

4. Put in equation for length to get area as a function of width:
= 8W - W^2.

Answer 5

Perimeter = 2*(w+l) = 16

or l = 8-w

Thus Area = w*l = w*(8-w).