Austin bicycles 9 kilometers west to get from his house to school. After school, he bicycles

12 kilometers north to his friend Trey's house. How far is Austin's house from Trey's

house, measured in a straight line?

15 km

Step-by-step explanation:

If you draw yourself a sketch, you will see that the geometry is that of a right triangle with sides 9 km and 12 km. The question is asking the length of the hypotenuse. You can figure this using the Pythagorean theorem, or using your knowledge of right triangles.

The given legs, 9 and 12, have the ratio 3 : 4, so are the legs of a 3-4-5 right triangle with a scale factor of 3 km. The "5" (hypotenuse) will correspond to a length of 5*3 km = 15 km.

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Using the Pythagorean theorem formula ...

AT² = AS² + ST²

AT² = (9 km) ² + (12 km) ² = 225 km²

AT = √ (225 km²) = 15 km

It is 15 km from Austin's house to Trey's house in a straight line.