Question

A farmer wants to seed and fence a section of land. Fencing costs $27 per yard. Grass seed costs $2 per square foot. How much does it cost to fence and seed the pasture?

A land for farming has a square-shaped piece of land and an isosceles triangular shaped piece of land that share a base. The square piece of land has a side length of 450 feet. The triangle has legs of 255 feet and height of 120 feet.

Answer 1

To fence and seed the farmer's land, the total fenced perimeter is 770 yards, and the total area for seeding is 229,500 square feet. The total cost for fencing is $20,790 and for seeding is $459,000, adding up to a total cost of $479,790.

Step-by-step explanation:

To calculate the total cost to fence and seed the square and isosceles triangular sections of land owned by the farmer, we first need to determine the perimeter of the land to be fenced and the area that needs to be seeded.

Square Piece of Land

The side length of the square is 450 feet, so its perimeter is:

Perimeter (square) = 4 × side = 4 × 450 feet = 1800 feet

Area (square) = side × side = 450 feet × 450 feet = 202500 square feet

Triangular Piece of Land

For the triangular piece of land, we have two sides with the length of 255 feet. The base of the triangle is shared with one side of the square, so it's not included again in fencing calculations. However, we'll need the area to calculate the seeding costs.

Perimeter (triangle sides only) = 2 × 255 feet = 510 feet

Area (triangle) = 0.5 × base × height = 0.5 × 450 feet × 120 feet = 27000 square feet

Total Costs

The total perimeter needing fencing is the sum of the square's perimeter and the two sides of the triangle:

Total perimeter = 1800 feet + 510 feet = 2310 feet

Total area = 202500 square feet + 27000 square feet = 229500 square feet

Convert perimeter to yards (1 yard = 3 feet):

Total perimeter in yards = 2310 feet / 3 = 770 yards

Now, calculate the total costs:

Fencing cost = 770 yards × $27/yard = $20790

Seeding cost = 229500 square feet × $2/square foot = $459000

Total cost = Fencing cost + Seeding cost = $20790 + $459000 = $479790

Answer 2

$500625

Step-by-step explanation:

$27 per yard. Grass seed costs $2 per square foot. How much does it cost to fence and seed the pasture? A land for farming has a square-shaped piece of land and an isosceles triangular shaped piece of land that share a base. The square piece of land has a side length of 450 feet. The triangle has legs of 255 feet and height of 120 feet. area shape square = 450 *450 Square Area = 202500 SQft perimeter = 450* 4 =1800 Ft TRIANGLE = Hypotenuse is given by formula H=B√2 but height is already given = 120 and 255 area = Height * Base = 120 * 255 =Triangle Area = 30600 feet squared perimeter = 255 * 3 = 765 Ft fence perimeter is 765-255 = 510 feet total area = 202500+ 30600= 233100 square foot = 233100* $2 = (*2) = $466200 total fence = 765+510 = 1275 feet = 1275(*$27) = $34425 Total cost = 466200+34425 = $500625