Question

Beginning in Town A, Biker Bob rides his bike 10 miles west, 3 miles north,S miles east, and then 9 miles north, to Town B. How far apart are Town A and Town B? (Assume perfectly flat terrain.)

• A. $12$
• B. $11$
• C. $13$
• D. $15$

Answer 1

The correct option is C $13$

13 miles: If you draw a rough sketch of the path Biker Bob takes, as shown to the right, you can see that the direct distance from A to B forms the hypotenuse of a right triangle. The short leg (horizontal) is 10 -5 = 5 miles, and the long leg (vertical) is 9 + 3 = 12 miles. Therefore, you can use the Pythagorean theorem to find the direct distance from A to B:

$5^2+{12}^2=c^2$

$25+144=c^2$

$c^2=169$

$c=13$

Option C