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To drive from Silver City to Urbana, you have to go 15 miles due north to Wakefield. Then you turn left and go due west 10 miles to Urbana. If there were a road directly from Silver City to Urbana, how far a drive, in miles, would this be (to the nearest mile)?

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Question:

A
18

explanation

Because due north and due west form a right angle, the three cities form a right triangle. The distance from Silver City to Urbana is the hypotenuse of this right triangle. The legs of this right triangle are 15 and 10 miles. According to the Pythagorean theorem, \(hypotenuse^2=15^2+10^2=225+100=325\) Therefore, the length of the direct route is \(\sqrt{325}\) , which is 18, to the nearest mile.

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