In order to get to school carly must first take take a bus 12 miles due east. she then gets off that bus and take another bus 9 miles due north in order to reach the school building. if there were a single bus traveling northeast that could take directly to the school from home, how many miles shorter would her route be.
do you know about a 3-4-5 right triangle?
hint: 9=3*3 and 12=3*4 . . .
To solve this problem, we can use the concept of the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
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.