Question

after school, duncan skateboards directly from school to a candy store and then from the candy store to an ice cream parlor. the candy store is 12 kilometers south of the school and the ice cream parlor is 9 kilometers east of the candy store. what is the straight - line distance between the school and the ice cream parlor? \\(\square\\) kilometers

Explanation:

Step1: Identify the triangle type

The path from school to candy store (south, 12 km) and candy store to ice cream parlor (east, 9 km) are perpendicular. So, the straight - line distance from school to ice cream parlor is the hypotenuse of a right - triangle with legs \(a = 12\) km and \(b=9\) km.

Step2: Apply the Pythagorean theorem

The Pythagorean theorem states that for a right - triangle with legs \(a\) and \(b\) and hypotenuse \(c\), \(c=\sqrt{a^{2}+b^{2}}\). Substitute \(a = 12\) and \(b = 9\) into the formula:

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Answer:

15