Final answer:
The dimensions of the rectangle are a width of 6 and a length of 18; found by using the given perimeter and the relationship between length and width.
Step-by-step explanation:
To find the dimensions of the rectangle, let's denote its width as w and its length as l. According to the problem, the length is three times the width, so l = 3w. The perimeter (P) is given by the formula P = 2l + 2w. Plugging in the relationship between length and width, the formula becomes P = 2(3w) + 2w, which simplifies to P = 6w + 2w, or P = 8w. We are told that the perimeter is 48, so we can set up the equation: 8w = 48.
To find the width, we divide both sides of the equation by 8: w = 48 / 8. Solving for w, we find that w = 6. Now that we have the width, we can find the length by using the relationship l = 3w: l = 3 × 6, which means l = 18. So, the dimensions of the rectangle are a width of 6 and a length of 18.