Your friend's house is 4.5 miles north and 6 miles east of the firehouse. how far is your friend's house from the firehouse?

9514 1404 393

  7.5 miles

Step-by-step explanation:

The distances are in the ratio 4.5/6 = 3/4, suggesting that the triangle whose sides are the north distance, the east distance, and the straight-line distance is a 3-4-5 right triangle. The scale factor is 4.5/3 = 1.5. So, the straight-line distance from the firehouse is 1.5×5 = 7.5 miles.

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Maybe you're not familiar with a 3-4-5 right triangle, so you need to compute the distance using the Pythagorean theorem. Then the straight-line distance (hypotenuse) is given by ...

  d² = 4.5² +6²

  d² = 20.25 +36 = 56.25

  d = √56.25 = 7.5

The straight-line distance from the firehouse to your friend's house is 7.5 miles.

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