Question

how long is the shortest route from asheboro to fort jennings using the roads shown? if necessary, round your answer to the nearest tenth. miles

Explanation:

Step1: Calculate the vertical distance from Asheboro to Fisher

The vertical distance from Asheboro to Fisher is $7$ miles.

Step2: Calculate the horizontal distance from Fisher to the point directly below Fort Jennings

The horizontal distance from Fisher to the point directly below Fort Jennings is $16$ miles.

Step3: Use the Pythagorean theorem to find the straight - line distance from Asheboro to Fort Jennings

The vertical distance from Asheboro to the horizontal line of Fort Jennings is $7 + 3=10$ miles. According to the Pythagorean theorem $a^{2}+b^{2}=c^{2}$, where $a = 10$ and $b = 16$. So $c=\sqrt{10^{2}+16^{2}}=\sqrt{100 + 256}=\sqrt{356}\approx18.9$ miles.

Answer:

$18.9$