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Darrell is playing hide-and-seek with Victor and Scarlett. Victor is hiding $16\,\text{meters}$ south of Darrell, and Scarlett is hiding $12\,\text{meters}$ east of Victor. How far apart are Darrell and Scarlett? $\newline$ $\_\_\_\_\_$ meters

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Pythagorean theorem: word problems

Full solution

Q. Darrell is playing hide-and-seek with Victor and Scarlett. Victor is hiding

16\,\text{meters}

south of Darrell, and Scarlett is hiding

12\,\text{meters}

east of Victor. How far apart are Darrell and Scarlett?

\newline

\_\_\_\_\_

meters

Identify Positions: Identify the positions of Victor and Scarlett relative to Darrell. Victor is $16$ meters south of Darrell, and Scarlett is $12$ meters east of Victor.
Visualize as Triangle: Visualize the scenario as a right triangle where Darrell and Scarlett form the hypotenuse. The distance from Darrell to Victor is one leg ( $16$ meters), and the distance from Victor to Scarlett is the other leg ( $12$ meters).
Apply Pythagorean Theorem: Apply the Pythagorean Theorem to find the distance between Darrell and Scarlett. Let d be the distance between Darrell and Scarlett. $\newline$ $d^2 = 16^2 + 12^2$
Calculate Squares: Calculate the squares of the legs. $\newline$ $16^2 = 256$ $\newline$ $12^2 = 144$ $\newline$ $d^2 = 256 + 144$
Add Squares: Add the squares of the legs. $\newline$ $d^2 = 400$
Find Distance: Find the square root of $400$ to get the distance d. $\newline$ $d = \sqrt{400}$ $\newline$ $d = 20$ meters

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