Final answer:
The width of the rectangle is 6 units and the length is 12 units. The area of the rectangle is 72 square units.
Step-by-step explanation:
To solve this problem, let's assign a variable to represent the width of the rectangle. Let's call it 'w'. According to the problem, the length of the rectangle is twice its width, so the length can be represented as '2w'.
The perimeter of a rectangle is given by the formula P = 2w + 2(2w) = 36. Simplifying the equation, we have 6w = 36. Dividing both sides by 6, we find that w = 6.
Now that we know the width, we can find the length by multiplying it by 2. The length is therefore 2w = 2(6) = 12.
The area of a rectangle is given by the formula A = length x width. Substituting the values we found, we get A = 12 x 6 = 72 square units. Therefore, the area of the rectangle is 72.