Question

Consider a rectangle with the following property.

Perimeter: 84 meters
Let w represent the width of the rectangle and let A represent the area of the rectangle. Write an equation for A in terms of w.
A(W) =

Answer 1

The equation for A in terms of w is A(w) = 42w - w²

How to determine the equation for A in terms of w

Let l represent the length of the rectangle. We know that the perimeter of the rectangle is 84 meters, so we can write the equation:

2l + 2w = 84

Solving for l in terms of w, we get:

l = 42 - w

We know that the area of the rectangle is A = lw, so we can substitute the expression for l in terms of w to get:

A(w) = (42 - w)w

Expanding, we get:

A(w) = 42w - w²

Hence, the equation for A in terms of w is A(w) = 42w - w²