A rectangle has perimeter 12 m. Express the area A of the rectangle as a function of the length, L, of one of its sides.

Sure, let's break it down:

1. The perimeter of a rectangle is given by the formula P = 2L + 2W, where L is the length and W is the width of the rectangle.

2. Given that the perimeter is 12m, we can express the width W in terms of the length L as follows: 12 = 2L + 2W. Solving for W, we get W = (12 - 2L) / 2 = 6 - L.

3. The area of a rectangle is given by the formula A = LW.

4. Substituting W from step 2 into the area formula, we get A = L * (6 - L).

So, the area A of the rectangle as a function of the length L of one of its sides is A(L) = L * (6 - L).