Question

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) 100
b) 98
c) 40
d) 200
e) 144

Answer 1

To find the straight-line distance between Hermansville and Melville, we can use the Pythagorean Theorem. The straight-line distance is approximately √20800 miles, which is approximately 144 miles.

Step-by-step explanation:

To find the straight-line distance between Hermansville and Melville, we can use the Pythagorean Theorem. The distance north is 120 miles and the distance west is 80 miles. So, the straight-line distance is the hypotenuse of a right triangle with legs of 120 miles and 80 miles. Using the formula c^2 = a^2 + b^2, where c represents the hypotenuse, a represents the length of one leg, and b represents the length of the other leg, we can calculate the straight-line distance.

Plugging in the values, we have c^2 = 120^2 + 80^2. Evaluating this equation, we get c^2 = 14400 + 6400 = 20800. Taking the square root of both sides, we find c = √20800. Therefore, the straight-line distance between Hermansville and Melville is approximately √20800 miles, which is approximately 144 miles.