Question

Terry owns a triangular piece of land that has three corner fence poles at A, B,and C. The three poles are plotted on a grid in units of feet at A(1000, 8000), B(6000, 7000), and C(5000, 1000). Terry wants to fence his land. To the nearest foot, how much fence does he need?

Answer 1

Answer: 19,244 ft

Step-by-step explanation:

1. To solve this exercise you can apply the formula for calculate the distance between two points, which is:

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

2. Then:

$d_{AB}=\sqrt{(6,000-1000)^{2}+(7,000-8,000)^{2}}=5,099.01$

$d_{AC}=\sqrt{(5,000-1000)^{2}+(1,000-8,000)^{2}}=8,062.25$

$d_{AC}=\sqrt{(5,000-6000)^{2}+(1,000-7,000)^{2}}=6,082.76ft$

3. Add the distance obtained to calculate the perimeter of the triangle. Therefore, the fence needed to the nearest food is:

$P=5,099.01ft+8,062.25ft+6,082.76ft=19,244.02ft=19,244ft$