### Answer:

Choice C

Level of Difficulty E

**M** H

The diagram shows the path that Diane travels, but then asks how much shorter the trip would be if she went directly from

*A* to

*D*. This distance is actually called the displacement, and is an important concept in

physics.

The distance she traveled on the path she chose was 16 + 15 + 4 = 35 miles. Now let's get the distance from

*A* to

*D*. Then, we can take the difference between the two.

The key to getting the distance from

*A* to

*D* is to form a large rectangle that contains the entire diagram, with the lower left corner of the rectangle at

*A*, and the upper right corner at

*D*. Now you will notice that the direct path we are interested in is the diagonal of the rectangle. This diagonal is also the hypotenuse of a right triangle whose legs have length 20 (16+4) and 15. We can apply Pythagorean's Theorem to find the length of the hypotenuse:

C

^{2} = A

^{2} + B

^{2}
C

^{2} = 20

^{2} + 15

^{2}
C

^{2} = 400 + 225

C

^{2} = 625

C = 25

Now we can answer the question "If she were able to travel from

*A* to

*D* directly, how much shorter, in miles, would the trip be?" All we need to do is take the difference between the path she actually walked (35 miles) and the straight-line distance between

*A* and

*D* (25 miles) which gives 10 miles, or choice C.

You might also have noticed that the legs of a right triangle with lengths 15 (3X5) and 20 (4X5) must be the legs of a 3-4-5 right triangle, so the hypotenuse must be 25 (5X5).

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