Answer:
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.
