Let's break down the problem:

• The length of a new rectangular playing field is 5 yards longer than double the width.
• The perimeter of the field is 250 yards.
• You need to find the dimensions (the width and length).

Let’s define the variables:

• Let $w$ be the width of the rectangular field in yards.
• The length of the field is $2w + 5$ yards (because it's 5 yards longer than double the width).

Formula for the perimeter of a rectangle:

The perimeter $P$ of a rectangle is given by: $P = 2 \times (\text{length} + \text{width})$

Substitute the given perimeter (250 yards) and the expressions for length and width: $250 = 2 \times \left( (2w + 5) + w \right)$

Solve the equation:

First, simplify the equation: $250 = 2 \times (3w + 5)$ $250 = 6w + 10$ Subtract 10 from both sides: $240 = 6w$ Now divide both sides by 6: $w = 40$

Find the length:

Substitute $w = 40$ into the expression for the length: $\text{Length} = 2w + 5 = 2(40) + 5 = 80 + 5 = 85$

Final dimensions:

• Width = 40 yards
• Length = 85 yards

Would you like more details or have any questions about this solution?

Here are 5 related questions:

1. How would the dimensions change if the perimeter were 300 yards?
2. What would happen if the length were triple the width instead of double plus 5 yards?
3. Can you solve this problem using the area of the rectangle?
4. How does changing the perimeter affect the relationship between width and length?
5. What other real-world problems could use a similar setup for their solution?

Tip: Always double-check that your variables correctly match the conditions given in word problems.