A gardner plans to build a fence around his 24 by 12 foot rectangular vegetable garden. fencing for the garden can be purchased in 50 foot, 75 foot, or 100 foot rolls. which roll of fencing should the gardner buy
To determine which roll of fencing the gardener should buy, we need to calculate the total amount of fencing required to enclose the garden.
The garden is in the shape of a rectangle, with dimensions of 24 by 12 feet. In order to enclose the garden, we need to calculate the perimeter of the rectangle.
The perimeter of a rectangle can be found by adding up all four sides. In this case, we have two sides measuring 24 feet and two sides measuring 12 feet.
Perimeter = 2 * (length + width)
Substituting the values into the equation:
Perimeter = 2 * (24 + 12)
Perimeter = 2 * 36
Perimeter = 72 feet
So, the gardener needs a fence with a length of 72 feet to enclose the garden.
Now, let's compare this requirement with the available fencing roll sizes:
- 50-foot roll: This roll is not long enough to enclose the entire garden, as it falls short by 22 feet (72 - 50).
- 75-foot roll: This roll is long enough to enclose the garden, but it will have an excess of 3 feet (75 - 72).
- 100-foot roll: This roll is long enough to enclose the garden, and it allows for an extra 28 feet (100 - 72), which can be used for future repairs or if any mistakes occur during installation.
Based on these calculations, the best roll of fencing for the gardener to buy would be the 100-foot roll, as this provides sufficient length to enclose the garden and allows for some extra footage.
P = 2L + 2W
P = 2(24) + 2(12)
P = 72 feet