A rectangle has an area of 72 square inches. The length of the longest side is twice the length of the shortest side. What is the length of the rectangle?

L=2W,

L*W=72
(2W)*W = 72
W²=72/2=36
Solve for W (width) and hence calculate length L.

what the hell

To find the length of the rectangle, let's start by understanding the given information. We know the area of the rectangle is 72 square inches, and the length of the longest side is twice the length of the shortest side.

Let's assume the length of the shortest side is "x" inches. According to the given information, the length of the longest side would be 2x inches.

The formula to find the area of a rectangle is length multiplied by width. In this case, the length is 2x and the width is x.

So, we can write the equation as follows:

2x * x = 72

Simplifying the equation:

2x^2 = 72

Divide both sides of the equation by 2:

x^2 = 36

Now, we can solve for x by taking the square root of both sides of the equation:

sqrt(x^2) = sqrt(36)

Thus, we have two possibilities for x: x = 6 or x = -6. Since the length cannot be negative, we discard x = -6.

Therefore, the length of the shortest side (x) is 6 inches. And since the length of the longest side is twice the length of the shortest side, the longest side is 2 * 6 = 12 inches.

Hence, the length of the rectangle is 12 inches.