Answer:
24 kilometers.
Step-by-step explanation:
The shortest path between two points is a straight segment that connects the two points.
Refer to the diagram attached. The 6-km segment and the 8-km segment are normal to each other. Together with the segment that joins the library and the house, the three segments now form a right triangle.
- The two shorter segments are the two legs, and
- The longer segment that joins the library and the house is the hypotenuse.
The length of the hypotenuse can be found with the Pythagorean Theorem.
.
The length of the round-trip will equal to the sum of the length of the three segments:
.
C = 3b+2d is the same as 3b+2d = C
Let's isolate d. To do this, we first need to subtract 3b from both sides
3b+2d = C
3b+2d-3b = C-3b
2d = C-3b
Then divide both sides by 2
2d = C-3b
2d/2 = (C-3b)/2
d = (C-3b)/2
Take note of the parenthesis as they are very important. We want to divide ALL of C-3b over 2. We don't want to just divide -3b over 2.
The answer choices you have aren't 100% clear but I have a feeling your teacher meant to say d = (C-3b)/2 instead of d = C-3b/2 for choice A
If that assumption is correct, then the answer is choice A.
I think it may be 1,680B but I'm not too sure...