Final answer:
a. The gardener needs 4 bags of grass seed which cost a total of $110. b. The cost of fencing to enclose the area is $278.28. c. The gardener needs 119 fence posts which will cost a total of $379.61.
Step-by-step explanation:
a. To find the area of the park, which is a right triangle, we will use the formula: Area = 1/2 * base * height. Plugging in the values, we have:
Area = 1/2 * 150 ft * 200 ft = 15000 ft².
Now, to determine the number of bags of grass seed needed, we divide the area by the coverage of each bag:
Number of bags = Area / Coverage = 15000 ft² / 3750 ft² = 4 bags.
To calculate the total cost, we multiply the number of bags by the cost per bag: Total cost = Number of bags * Cost per bag = 4 bags * $27.50/bag = $110.
b. To enclose the area of the park, we need to find the perimeter of the triangle. The perimeter of a triangle is the sum of its three sides.
In this case, the perimeter is given as the sum of the base, height, and the third side: Perimeter = base + height + third side = 150 ft + 200 ft + 250 ft = 600 ft.
Now, we can calculate the number of rolls of wire fencing needed by dividing the perimeter by the length of each roll: Number of rolls = Perimeter / Length per roll = 600 ft / 50 ft = 12 rolls.
To find the total cost, we multiply the number of rolls by the cost per roll: Total cost = Number of rolls * Cost per roll = 12 rolls * $23.19/roll = $278.28.
c. To determine the number of fence posts needed, we need to find the number of spaces between each fence post.
This can be done by dividing the perimeter by the spacing between each post: Number of spaces = Perimeter / Spacing = 600 ft / 5 ft = 120 spaces.
Since we have one post at the starting point, we subtract one from the number of spaces to get the number of posts needed: Number of posts = Number of spaces - 1 = 120 posts - 1 = 119 posts.
To calculate the total cost, we multiply the number of posts by the cost per post: Total cost = Number of posts * Cost per post = 119 posts * $3.19/post = $379.61.