Question

Runners at a cross-country meet run 2 miles south and then 4 miles west from the starting line. Determine the shortest straight path they must run to get back to the starting line.


a) 6 miles

b) square root of 6 miles

c) square root of 12 miles

d) square root of 20 miles

Answer 1

To determine the shortest straight path back to the starting line, we can use the Pythagorean theorem. The distance south and west can be seen as the two sides of a right triangle.

Let's call the distance south = x miles and the distance west = y miles.

According to the given information, x = 2 miles and y = 4 miles.

Using the Pythagorean theorem, we have:

hypotenuse^2 = x^2 + y^2
hypotenuse^2 = 2^2 + 4^2
hypotenuse^2 = 4 + 16
hypotenuse^2 = 20

To find the hypotenuse, we take the square root of both sides:
hypotenuse = √20 miles

Therefore, the shortest straight path they must run to get back to the starting line is √20 miles, which corresponds to answer choice d.