A rectangle has a perimeter of 36 cm and is twice as long as it is wide. Find its area.

Problem: Find the area of a rectangle with a perimeter of $36\text{ cm}$ that is twice as long as it is wide.

Steps

1. Define variables
   $$l = 2w$$
2. Substitute into the perimeter formula
   $$2(l + w) = 36$$
3. Substitute $l = 2w$ into the equation
   $$2(2w + w) = 36$$
4. Combine like terms
   $$2(3w) = 36$$
5. Multiply
   $$6w = 36$$
6. Divide both sides by 6
   $$w = 6$$
7. Find the length
   $$l = 2(6) = 12$$
8. Calculate the area
   $$\text{Area} = l \times w = 12 \times 6$$
9. Multiply for the final area
   $$\text{Area} = 72$$