Question

A carpenter is building a rectangular shed with a fixed perimeter of 56 ft. What are the dimensions of the largest shed that can be​ built? What is its​ area?

Answer 1

There is no largest shed that can be built with a fixed perimeter of 56 ft.

Step-by-step explanation:

To find the dimensions of the largest shed, we need to find the length and width that will give us the maximum area. Since the perimeter is fixed at 56 ft, let's assume the length is x, then the width would be (56 - 2x).

Perimeter of the rectangle = 2(x + (56 - 2x)) = 4x + 112 - 4x = 112
Set the perimeter equal to 112 and solve for x: 4x + 112 = 112
4x = 0
x = 0
The dimensions of the largest shed that can be built would be 0 ft by 0 ft, which is not possible. Therefore, there is no largest shed that can be built with a fixed perimeter of 56 ft.