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.
[tex]\begin{aligned}\text{Hypotenuse} &= \sqrt{(\text{Leg 1})^{2} + (\text{Leg 2})^{2}}\\&= \sqrt{6^{2} + 8^{2}}\\&= \sqrt{36 + 64} \\&= \sqrt{100}\\&= \rm 10\;km\end{aligned}[/tex].
The length of the round-trip will equal to the sum of the length of the three segments: [tex]\rm 6\;km + 8\;km + 10\;km = 24\;km[/tex].
