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Three ballet dancers are positioned on stage. Edwin is straight behind Danielle and directly left of Katy. If Danielle and Edwin are $12$ meters apart, and Katy and Danielle are $13$ meters apart, what is the distance between Edwin and Katy? $\newline$ $\_\_\_\_$ meters

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Pythagorean theorem: word problems

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Q. Three ballet dancers are positioned on stage. Edwin is straight behind Danielle and directly left of Katy. If Danielle and Edwin are

12

meters apart, and Katy and Danielle are

13

meters apart, what is the distance between Edwin and Katy?

\newline

\_\_\_\_

meters

Recognize Triangle Positions: Recognize the positions of the dancers form a right triangle, with Edwin and Danielle forming one leg, and Danielle and Katy forming the other leg. Edwin and Katy's distance will be the hypotenuse.
Use Pythagorean Theorem: Use the Pythagorean Theorem to find the distance between Edwin and Katy. The theorem states that in a right triangle, the square of the length of the hypotenuse $c$ is equal to the sum of the squares of the lengths of the other two sides $a$ and $b$ .
Plug in Known Distances: Plug in the known distances into the Pythagorean Theorem. Let's call the distance between Edwin and Katy ' extit{c}', between Danielle and Edwin ' extit{a}' ( $12$ meters), and between Danielle and Katy ' extit{b}' ( $13$ meters). $\newline$ So, $a^2 + b^2 = c^2$ becomes $12^2 + 13^2 = c^2$ .
Calculate Squares: Calculate the squares of $12$ and $13$ . $12^2 = 144$ and $13^2 = 169$ .
Add Squares: Add the results of the squares to find $c^2$ . So, $144 + 169 = c^2$ gives us $313 = c^2$ .

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