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
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.