Question

Diana has available 280 yards of fencing and wishes to enclose a rectangular area. (a) Express the area (A) of the rectangle as a function of the width (W) of the rectangle.

Answer 1

The area of a rectangle can be expressed as a function of the width when given the amount of available fencing. To find the area, consider the perimeter of the rectangle, which is equal to the sum of the lengths of all four sides. In a rectangle, opposite sides are equal in length.

Step-by-step explanation:

The area of a rectangle, A, can be expressed as a function of the width, W, when given the amount of available fencing. In this case, Diana has 280 yards of fencing. To find the area, we need to consider the perimeter of the rectangle, which is equal to the sum of the lengths of all four sides. In a rectangle, opposite sides are equal in length.

Let's assume the rectangle has a length of L and a width of W. The perimeter P is given as:
P = 2L + 2W

Since Diana has 280 yards of fencing, we can write the equation:
2L + 2W = 280

Now, we need to express the area A as a function of the width W. We can solve the equation above for L:
L = (280 - 2W) / 2
Substitute this value of L into the area formula A = L * W:
A = ((280 - 2W) / 2) * W
Simplifying further:
A = (280W - 2W²) / 2
You can simplify the expression further if required.

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