Kelly is driving to a friend's house. She drives 15 miles north and then drives 18 miles west

Question

1. How many miles does Kelly have to drive to get to her friend's house?
2. If there were a direct road (straight line) between Kelly's house and her friend's house, how far would Kelly have to drive?
3. Which route is shorter? How much shorter is it?

Answer 1

1) SHe drives 33 miles

2)

sqrt( 15^2 + 18^2) = sqrt( 225 + 324) = sqrt( 549) = sqrt( 3 * 183) = sqrt( 3* 3 * 61)

= 3 * sqrt(61)

3) direct route is 33 - 3 * sqrt(61) shorter, just over 9.5 miles shorter