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After school, Tyler skateboards directly from school to a game store and then from the game store to a movie theater. The game store is $12$ kilometers south of the school and the movie theater is $5$ kilometers east of the game store. What is the straight-line distance between the school and the movie theater? $\newline$ $\_\_\_\_$ kilometers

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Pythagorean Theorem and its converse

Full solution

Q. After school, Tyler skateboards directly from school to a game store and then from the game store to a movie theater. The game store is

12

kilometers south of the school and the movie theater is

5

kilometers east of the game store. What is the straight-line distance between the school and the movie theater?

\newline

\_\_\_\_

kilometers

Triangle Formation: Tyler's path forms a right triangle with the legs being the distances from the school to the game store and from the game store to the movie theater.
Legs and Hypotenuse: Legs of the triangle: $12\,\text{km}$ (south), $5\,\text{km}$ (east). We need to find the hypotenuse.
Pythagorean Theorem: Use the Pythagorean Theorem: $a^2 + b^2 = c^2$ , where $a$ and $b$ are the legs and $c$ is the hypotenuse.
Plug in Values: Plug in the values: $12^2 + 5^2 = c^2$ .
Calculate Sum: Calculate: $144 + 25 = c^2$ .
Square Root Calculation: Add the values: $169 = c^2$ .
Final Hypotenize: Take the square root of both sides: $\sqrt{169} = c$ .
Final Hypotenize: Take the square root of both sides: $\sqrt{169} = c$ . Calculate the square root: $c = 13$ .

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