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.
6 miles
square root of 6 miles
square root of 12 miles
square root of 20 miles
The shortest straight path they must run to get back to the starting line can be found using the Pythagorean theorem. The distance traveled south and west can be considered as the legs of a right triangle, where the hypotenuse represents the shortest straight path.
Using the Pythagorean theorem, we can find the length of the hypotenuse:
hypotenuse^2 = (2 miles)^2 + (4 miles)^2
hypotenuse^2 = 4 + 16
hypotenuse^2 = 20
Taking the square root of both sides to solve for the length of the hypotenuse:
hypotenuse = square root of 20 miles
Therefore, the shortest straight path they must run to get back to the starting line is the square root of 20 miles.