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 bridge are constructed from point

Explanation:

Step1: Identify the coordinates of the vertices

Let \(Q=(0,0)\), \(P=(0,50)\), \(R=(80,0)\)

Step2: Use the distance formula \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\) to find the lengths of the sides

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

Step3: Calculate the perimeter

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

Answer:

224