Question

Theo, Nancy, and Mary each drove separately to meet at their grandmother's house for
dinner. Theo drove 50 miles, Nancy drove 2840 miles, and Mary's route is shown below.
The bottom of the triangle is 13 mil
The side of the triangle is 48 mi
Mary drove approximately ______ miles to her grandmother's house.
The order of their drives from shortest to longest is_______

Answer 1

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:

1. Mary: approximately 49.73 miles
2. Theo: 50 miles
3. Nancy: 2840 miles

Thus, the order of their drives from shortest to longest is **Mary, Theo, Nancy**.