Question

Crystal has a running course marked out for her daily run. She starts this run by heading due north for one mile. She then runs northeast for one mile, then southeast for one mile. The last portion of her run takes her on a straight line back to where she started. How far, in miles, is this last portion of her run?

$1$

$\sqrt{2}$

$\sqrt{3}$

$2$

$2\sqrt{2}$

Solution:

From the diagram, we see that the distance traveled is the hypotenuse of a right triangle.

One of the legs is just $1$ from running due north. The other leg is $\sqrt{1^2 + 1^2} = \sqrt2.$

The final distance is then $\sqrt{\sqrt2^2 + 1^2} = \sqrt3.$

Thus, C is the correct answer.

2010 AMC 10A Problem 7

Solution:

Problem 7 in Other Years