Final answer:
Two equivalent expressions for the perimeter of a rectangle are 6 times the width and 2 times the sum of the length and the width.Perimeter of rectangle with width (w) and length (2w): P = 6w or P = 2(2w + w).
Step-by-step explanation:
The perimeter of a rectangle is the sum of all its sides. Let's say the width of the rectangle is w inches. According to the problem, the length of the rectangle is twice its width, so the length is 2w inches. The perimeter is calculated by adding the lengths of all four sides, so for this rectangle, the perimeter is 2w + 2w + w + w. Simplifying this expression, we get 6w or 6 times the width.
Another equivalent expression for the perimeter of the rectangle is 2(l + w). Using the values we derived earlier, the length is 2w and the width is w. Substituting these values in the expression, we get 2(2w + w) which simplifies to 2(3w) or 6w.
Let the width of the rectangle be "w" units. Since the length is twice the width, the length is "2w" units. The perimeter (P) is the sum of all sides. Therefore, one expression for the perimeter is P = 2w + 2(2w), simplifying to P = 6w. Another expression is P = 2(2w + w), which also simplifies to P = 6w. Both expressions, 6w and 2(2w + w), are equivalent representations of the rectangle's perimeter.