Question

Suppose that you used a certain amount of fencing to enclose a rectangular region of width, w and that you wanted to write an expression to represent the area of the region in terms of t. What actions should you take to write an expression to represent the area of the region in terms of w?

1) Multiply the width by t
2) Divide the width by t
3) Add the width to t
4) Subtract the width from t

Answer 1

To express the area of a rectangular region in terms of width (w) when the perimeter (t) is known, solve for length (l) in terms of w and t, and then use the rectangular area formula A = w × l.

Step-by-step explanation:

To write an expression for the area of the rectangular region in terms of width (w) when you know the total amount of fencing (which represents the perimeter), you first need to express the length in terms of w.

Let's denote the total fencing used as t. The perimeter of a rectangle is 2 times the sum of its width and length (P = 2(w + l)).

Given the perimeter as t, you can solve for length (l) using the equation t = 2(w + l), which gives us l = t/2 - w. Now, to find the area (A), you multiply the width by the length: A = w × l or A = w × (t/2 - w), which is the area in terms of the width w.

Therefore, the correct option is 1) Multiply the width by t.