Question

Ralph owns a circular farm as shown. He is planning to fence a triangular pigpen ABC in the farm. Point M is the midpoint of the side CB. All dimensions are in yards. Given that the fence material cost $30 per yard, what is the total cost to fence the pigpen?

Answer 1

`Total = \$942`

Explanation:

Given

`A = (0,0)`

`C = (3,4)`

See attachment for farm

Required

The cost of fencing the farm

First, calculate the radius of the farm.

The radius is represented with AC.

So, we have:

`AC = √((x_1 - x_2)^2 + (y_1 - y_2)^2)` ---- distance formula

So, we have:

`AC = √((0 - 3)^2 + (0 - 4)^2)`

`AC = √((- 3)^2 + ( - 4)^2)`

`AC = √(9+16)`

`AC = √(25)`

`AC = 5`

Hence:

`r = 5` --- radius

Calculate the circumference of the circle

`C = 2\pi r`

`C = 2 * 3.14 * 5`

`C = 31.4yd`

If 1 yard costs $30, 31.4 yards will cost:

`Total = 31.4 * 30`

`Total = \$942`