Question

1. one route along flat terrain from hermansville to melville is to drive straight north from hermansville for 120 miles to jamestown, then, at jamestown, to drive straight west for 80 miles to melville. if a straight, flat road existed between hermansville and melville, approximately how many miles long would it be?

a. 200
b. 144
c. 100
d. 98
e. 40

Explanation:

Step1: Recognize the right - triangle

The path from Hermansville to Jamestown (120 miles) and from Jamestown to Melville (80 miles) forms the two legs of a right - triangle. Let \(a = 120\) and \(b=80\). The straight - line distance \(c\) from Hermansville to Melville is the hypotenuse of the right - triangle.

Step2: Apply the Pythagorean theorem

The Pythagorean theorem is \(c=\sqrt{a^{2}+b^{2}}\). Substitute \(a = 120\) and \(b = 80\) into the formula:

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Answer:

B. 144