We are given that the length of a rectangle is 3 times its width, and the perimeter is 64 inches. We need to find the dimensions (length and width) of the rectangle.

Let's denote the width of the rectangle as $w$. Then, the length of the rectangle would be $3w$ (since the length is 3 times the width).

The formula for the perimeter $P$ of a rectangle is: $P = 2 \times (\text{length} + \text{width})$ Substituting the given perimeter and expressions for the length and width, we get: $64 = 2 \times (3w + w)$ Simplifying the equation: $64 = 2 \times 4w$ $64 = 8w$ Now, solve for $w$: $w = \frac{64}{8} = 8$ So, the width of the rectangle is 8 inches.

Since the length is 3 times the width, the length is: $\text{Length} = 3 \times 8 = 24 \text{ inches}.$

Thus, the dimensions of the rectangle are:

• Width: 8 inches
• Length: 24 inches

Would you like a deeper explanation on any part of the solution?

Here are five related questions to expand on this:

1. How would the dimensions change if the perimeter was different but the length-width ratio stayed the same?
2. Can you find the area of this rectangle based on its dimensions?
3. What would happen if the length were instead 4 times the width? How would that affect the perimeter?
4. Can the perimeter be used to determine the dimensions if the ratio between length and width is unknown?
5. How do you calculate the diagonal of the rectangle based on its dimensions?

Tip: Always check that your calculated dimensions satisfy the original conditions, such as length-to-width ratio and perimeter, to avoid errors.