Question

Of all rectangles with a perimeter of 21 21​, which one has the maximum​ area? (give the​ dimensions.) let a be the area of the rectangle. what is the objective function in terms of the width of the​ rectangle, w?

Answer 1

To find the rectangle with the maximum area, we need to find the dimensions and write the objective function in terms of the width of the rectangle.

Step-by-step explanation:

To find the rectangle with the maximum area, we need to find the dimensions of the rectangle that will give us the maximum area. Let's assume the width of the rectangle is w. Since the perimeter of the rectangle is given as 21, we can write the equation:

2w + 2l = 21

We can rearrange this equation to solve for l:

2l = 21 - 2w

l = (21 - 2w)/2

The area of the rectangle can be calculated as:

A = w * l

Substituting the expression for l we obtained earlier:

A = w * (21 - 2w)/2

Expanding and simplifying this equation will give us the objective function in terms of the width w.

Answer 2

All you need to do is LxWxH