Question

problem solving a path goes around a triangular park, as shown. a. find the distance around the park to the nearest yard the distance is about yards b. a new path and a

Explanation:

Step1: Identify coordinates

Assume \(P=(0, 50)\), \(Q=(0,0)\), \(R=(80,0)\).

Step2: Calculate side - lengths

Use the distance formula \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\).
For \(PQ\): \(d_{PQ}=\sqrt{(0 - 0)^2+(50 - 0)^2}=50\).
For \(QR\): \(d_{QR}=\sqrt{(80 - 0)^2+(0 - 0)^2}=80\).
For \(PR\): \(d_{PR}=\sqrt{(80 - 0)^2+(0 - 50)^2}=\sqrt{6400 + 2500}=\sqrt{8900}\approx94.34\).

Step3: Calculate perimeter

\(P=d_{PQ}+d_{QR}+d_{PR}=50 + 80+94.34 = 224.34\approx224\).

Answer:

224