The perimeter of a rectangle is 24 inches. What is the number of square inches in the maximum possible area for this rectangle?
the maximum area is obtained when your rectangle is a square.
so let the side be s
4s = 24
s = 6
area = 36
To determine the maximum possible area of a rectangle with a given perimeter, we need to apply the concept of optimization. In this case, we can use the property of rectangles that states the maximum area occurs when the rectangle is a square.
Let's denote the length of the rectangle as L and the width as W. We know that the perimeter of a rectangle is given by the formula:
Perimeter = 2L + 2W
In this case, the perimeter is given as 24 inches, so we have:
24 = 2L + 2W
To find the maximum area, we need to maximize the product of the length and width, which is A = L * W.
Since we want the rectangle to be a square, we can set L = W, and substitute this into the perimeter equation:
24 = 2L + 2L
24 = 4L
L = 6
So, the length (L) and width (W) of this square-shaped rectangle are both 6 inches.
To find the area, we can use the formula:
Area = L * W
Area = 6 * 6
Area = 36 square inches
Therefore, the maximum possible area for this rectangle is 36 square inches.