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from his house Mike rides his bike 2 miles west and 10 miles north to the gym how much shorter is it to the gym if he rode in a straight-line path

from his house Mike rides his bike 2 miles west and 10 miles north to the gym how-example-1

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Using the rectangular route Mike rides 12 miles. If he rides diagonally the distance is √2²+10²=√4+100=√104.
The difference between the two routes is 12-√104=1.80 miles approximately.
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