30 40 50 60 70 80 150140130120110100 The graphic below shows a protractor, which

The dimensions of the rectangle that maximizes the area is 24 inches by 24 inches.

Step-by-step explanation:

We are given that a metallic bar with a length of 96 inches was used to make a rectangular frame.

And we want to find the dimensions of the frame that yields the maximum area.

Since the bar has a length of 96 inches, the perimeter of the rectangle must total 96. Let l represent the length of the rectangle and w its width. Hence:

Divide:

The area of the rectangle will be:

From the first equation, solve for either variable:

Substitute:

Distribute:

Since the area of the rectangle is represented with a quadratic equation with a negative leading coefficient, the maximum area will occur at its vertex point.

The vertex of a quadratic is given by:

In this case, a = -1, b = 48, and c = 0.

Then the length for which the maximum area occurs is:

And the width will be:

In conclusion, the dimensions of the rectangle that maximizes the area is 24 inches by 24 inches.