Darrell is playing hide-and-seek with Victor and Scarlett. Victor is hiding 16 meters south of Darrell, and Scarlett is hiding 12 meters east of Victor. How far apart are Darrell and Scarlett? _____ 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. \[ d^2 = 16^2 + 12^2 \] Calculate Squares: Calculate the squares of the legs. \[ 16^2 = 256 \] \[ 12^2 = 144 \] \[ d^2 = 256 + 144 \] Add Squares: Add the squares of the legs. \[ d^2 = 400 \] Find Distance: Find the square root of 400 to get the distance d. \[ d = \sqrt{400} \] \[ d = 20 \] meters

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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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Grade 8

Pythagorean theorem: word problems

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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