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

Answer:

$Total = \ 942$

Step-by-step 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:

$AC = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}$ ---- distance formula

So, we have:

$AC = \sqrt{(0 - 3)^2 + (0 - 4)^2}$

$AC = \sqrt{(- 3)^2 + ( - 4)^2}$

$AC = \sqrt{9+16}$

$AC = \sqrt{25}$

$AC = 5$

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:

$Total = 31.4 * 30$

$Total = \ 942$