We are given the following information:

1. The length of the rectangle is three times its width.
2. The perimeter of the rectangle is 56 yards.

We need to find both the length and width of the rectangle.

Step-by-step solution:

Let:

• $w$ = width of the rectangle
• $l = 3w$ = length of the rectangle (since the length is three times the width).

The formula for the perimeter of a rectangle is: $P = 2l + 2w$ Substituting the given perimeter (56 yards) and the expression for length $l = 3w$: $56 = 2(3w) + 2w$ Simplify the equation: $56 = 6w + 2w$ $56 = 8w$ Solve for $w$: $w = \frac{56}{8} = 7 \, \text{yd}$

Now that we know the width, we can find the length: $l = 3w = 3(7) = 21 \, \text{yd}$

Final Answer:

• Width = 7 yards
• Length = 21 yards

Would you like further details or explanations?

Here are 5 related questions for further practice:

1. What would be the dimensions of a rectangle if its perimeter was 80 yards and the length was four times the width?
2. How would you find the area of the rectangle given the width and length?
3. If the perimeter of a square is 64 yards, what is the length of one side?
4. How would the solution change if the length were twice the width instead of three times?
5. What if the perimeter was given in meters instead of yards, how would the calculations change?

Tip: Always start by defining variables clearly, especially in word problems, to avoid confusion during calculations.