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?

Question

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

Answer 1

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.