do you know about a 3-4-5 right triangle?
hint: 9=3*3 and 12=3*4 . . .
hint: 9=3*3 and 12=3*4 . . .
In this scenario, Carly's route forms a right triangle, with the 12-mile bus ride due east as one side and the 9-mile bus ride due north as the other side. The hypotenuse of this right triangle would be the distance directly from home to the school if there were a single bus traveling northeast.
To find the length of the hypotenuse, we can use the Pythagorean theorem equation: c^2 = a^2 + b^2, where c represents the hypotenuse and a and b represent the other two sides.
In this case, a = 12 miles and b = 9 miles. Plugging those values into the equation, we can solve for c:
c^2 = 12^2 + 9^2
c^2 = 144 + 81
c^2 = 225
c = √225
c = 15 miles
So, if there were a single bus traveling northeast directly to the school, Carly's route would be 15 miles shorter than her current route.