if the perimeter of a rectangular closet is 40 ft and the width is 1 ft less than half of the length, what are the length and width ?

A rectangular closet is three dimensional. It also has depth. Are you just considering the door to the closet?

W = L/2 - 1

2W + 2L = 40

Substitute L/2 - 1 for W in the second equation and solve for L. Insert that value into the first equation to solve for W. Check by putting both values into the second equation.

To find the length and width of the rectangular closet, we need to set up an equation using the given information.

Let's assume:
Length = L
Width = W

According to the problem, the perimeter of the closet is 40 ft. Since the perimeter of a rectangle is the sum of all four sides, we can write the equation:

2(L + W) = 40

Now, we also know that the width is 1 ft less than half of the length. So we can write the equation:

W = (1/2)L - 1

Let's solve this system of equations to find the values of L and W.

First, substitute the second equation into the first equation:

2(L + [(1/2)L - 1]) = 40

Simplify:

2(L + (1/2)L - 1) = 40
2(3/2L - 1) = 40
3L - 2 = 40

Solve for L:

3L = 40 + 2
3L = 42
L = 42/3
L = 14

Now, substitute the value of L back into the second equation to find W:

W = (1/2)L - 1
W = (1/2)(14) - 1
W = 7 - 1
W = 6

Therefore, the length of the rectangular closet is 14 ft, and the width is 6 ft.