a The distance around the park is the sum of the lengths of each line segment of the triangle. Each unit represents 10 yards. The horizontal and vertical line segments are 70 yards and 40 yards, respectively.
c The time it takes for the man to complete a run depends on the distance and his speed. Let's make a schematic diagram of the runner's path.
The lengths of PQ and RQ were determined in Part A. They are 40 yards and 70 yards.
Since PQ and QP describe the same line segment, QP is also 40 yards.
In Part B, we found the length of QM to be 40 yards too.
M is the midpoint of P and R, meaning it divides PR into two congruent line segments. We know, from previous calculations, that PR≈ 81 yards, so MR is
81/2=40.5 yards.
This gives us the following diagram.
The total distance ran is the sum of all of the relevant lengths.
40+40+40.5+70+40=230.5 yards
We know that his average speed was 150 yards per minute. Therefore, the run takes
230.5yards/150 yards per minute≈ 1.5 minutes.
