The cake perimeter is 72 inches. The length is 2 times the width, what is the area of the cake?

P = 2L + 2W

72 = 2(2w) + 2W

72 = 6W

12 = W
24 = L

A = 12 * 24

288

288 square inches

To find the area of the cake, we need to know the length and width. We are given that the perimeter of the cake is 72 inches and the length is 2 times the width.

Let's assign variables to represent the width (W) and the length (L) of the cake.

Since the length is 2 times the width, we can write L = 2W.

The perimeter of a rectangle is given by the formula: perimeter = 2(L + W).

In this case, the perimeter of the cake is 72 inches. So we can write the equation: 72 = 2(L + W).

Now, substitute the value of L from the given information (L = 2W) into the equation: 72 = 2(2W + W).

Simplify the equation: 72 = 2(3W).

Divide both sides of the equation by 2: 36 = 3W.

Now, solve for W by dividing both sides of the equation by 3: W = 36 / 3 = 12 inches.

We have found the width of the cake to be 12 inches. The length is 2 times the width, so L = 2W = 2 * 12 = 24 inches.

Finally, to find the area of the cake, use the formula: area = length * width.

Substituting the values, we get: area = 24 * 12 = 288 square inches.

Therefore, the area of the cake is 288 square inches.