Final answer:
The correct dimensions of the backyard, calculated using the given perimeter and the relationship between length and width, are Length: 84 feet and Width: 46 feet, which does not match any of the provided choices. The calculations were performed again to verify their accuracy.
Step-by-step explanation:
To find the dimensions of the yard, we first need to create equations based on the information given. Let the width be w feet. According to the problem, the length is 8 feet less than twice the width, so the length is 2w - 8 feet. The perimeter of the rectangle, which is the total fencing needed, is the sum of twice the width and twice the length. Therefore, the equation for the perimeter (P) is P = 2w + 2(2w - 8). Since we know that 260 feet of fencing is needed, we have:
260 = 2w + 2(2w - 8)
Solving for w, we get:
- 260 = 2w + 4w - 16
- 260 + 16 = 6w
- 276 = 6w
- w = 46
Now that we know the width is 46 feet, we can find the length:
Length = 2(46) - 8 = 92 - 8 = 84 feet
However, since none of the choices match these calculations, we have made an error. Let's double-check the arithmetic:
- 260 = 2w + 4w - 16
- 260 + 16 = 6w
- 276 = 6w
- w = 46 feet
- Length = 2(46) - 8 = 92 - 8 = 84 feet
Upon reviewing our calculations, it appears there was no error and the given choices are incorrect. However, the correct dimensions of the backyard based on the calculations would be Length: 84 feet, Width: 46 feet.