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sdas [7]
3 years ago
12

5. To get to the library from his house, Robert biked 6 kilometers due east and then

Mathematics
1 answer:
AURORKA [14]3 years ago
5 0

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.

\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}.

The length of the round-trip will equal to the sum of the length of the three segments: \rm 6\;km + 8\;km + 10\;km = 24\;km.

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