Final answer:
To find the dimensions of the playing field, we set up equations with the given relationships: the length is twice the width plus 7 yards, and the perimeter is 260 yards. Solving these, we find the width to be 41 yards and the length to be 89 yards.
Step-by-step explanation:
To find the dimensions of a rectangular playing field where the length (L) is 7 yards longer than double the width (W), and the perimeter (P) is 260 yards, we will set up equations using the given information:
Plugging in the first equation into the second, we have:
- 260 = 2(2W + 7) + 2W
- 260 = 4W + 14 + 2W
- 260 = 6W + 14
- 246 = 6W
- W = 41 yards
Now that we have the width, we can find the length:
- L = 2(41) + 7
- L = 82 + 7
- L = 89 yards
The dimensions of the playing field are 89 yards in length and 41 yards in width.