A new highway was built outside of Tri Town to relieve traffic on Route 1. How many miles are saved by traveling on the new highway to get from point A to point B?
The tri-town is in the shape of a right triangle A-B-C. The new highway A-B forms the hypotenuse, A-C is 12 miles and B-C is 5 miles.
A.
1 mile
B.
4 miles
C.
13 miles
D.
30 miles
C. 13 miles
Using the Pythagorean theorem, we can find the length of the new highway A-B:
A-C^2 + B-C^2 = A-B^2
12^2 + 5^2 = A-B^2
144 + 25 = A-B^2
169 = A-B^2
A-B = 13
So, by traveling on the new highway from point A to point B, 13 miles are saved.