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The total distance flown by the bird directly from the courthouse to the library, then from the library to the swimming pool, and then from the swimming pool back to the courthouse is 13 + √85 miles
Generally, distance is a scalar quantity . This means it has only magnitude but no direction.
Distance describes how much ground an object covers on motion.
Therefore, the total distance the bird flew is how much ground it covered during motion.
The library is 6 miles south of the courthouse and 7 miles west of the community swimming pool.
Distance from court house to the library = 6 miles
Distance from library to the swimming pool = 7 miles
we use Pythagoras's theorem to find the distance from the swimming pool back to the courthouse. Therefore
Distance from swimming pool to the court house = 7² + 6² = 49 + 36 = √85
Total distance travelled = 6 + 7 + √85 = 13 + √85 miles
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