To find Mary's driving distance given the dimensions of her route, we need to determine the length of the third side of the triangle. From the problem, we have the following information for Mary's route:
- One side (base) of the triangle = 13 miles
- Another side of the triangle = 48 miles
Assuming these two sides form a right triangle with the distance Mary drove as the hypotenuse, we can use the Pythagorean theorem to calculate her distance:
\[ c^2 = a^2 + b^2 \]
where \(c\) is the hypotenuse, and \(a\) and \(b\) are the other two sides.
In this case:
- \(a = 13\)
- \(b = 48\)
Now we can calculate:
\[ c^2 = 13^2 + 48^2 \] \[ c^2 = 169 + 2304 \] \[ c^2 = 2473 \] \[ c = \sqrt{2473} \approx 49.73 \text{ miles} \]
So, Mary drove approximately 49.73 miles to her grandmother's house.
Now, let's list the distances driven by each person:
- Theo: 50 miles
- Nancy: 2840 miles
- Mary: approximately 49.73 miles
To determine the order of their drives from shortest to longest:
- Mary: approximately 49.73 miles
- Theo: 50 miles
- Nancy: 2840 miles
Thus, the order of their drives from shortest to longest is Mary, Theo, Nancy.