Question

relative to francos home, ashland is 6.4 miles due north and dayton is 5.7 miles due east. one day, franco decides to run some errands that will require him to leave home and drive to ashland, then go directly to dayton, and finally return home. how long of a drive will he be making? if necessary, round to the nearest tenth. miles

Explanation:

Step1: Find the distance from Ashland to Dayton

Since Ashland is north and Dayton is east of Franco's home, the three locations form a right - triangle. Use the Pythagorean theorem \(c=\sqrt{a^{2}+b^{2}}\), where \(a = 6.4\) and \(b=5.7\).

$$c=\sqrt{6.4^{2}+5.7^{2}}=\sqrt{40.96 + 32.49}=\sqrt{73.45}\approx8.6$$

Step2: Calculate the total driving distance

The total distance \(d\) is the sum of the three sides of the triangle. The three sides are \(6.4\), \(5.7\), and approximately \(8.6\).

$$d=6.4 + 5.7+8.6=20.7$$

Answer:

\(20.7\)