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Three students are sitting on a school bus. Billy is $4\,\text{meters}$ directly behind Sidney and $3\,\text{meters}$ directly left of Gordon. Billy makes a paper airplane and throws it to Sidney. Sidney throws the airplane to Gordon, who throws it back to Billy. How far has the paper airplane traveled? $\newline$ $\_\_\_\_\_$ meters

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Pythagorean theorem

Full solution

Q. Three students are sitting on a school bus. Billy is

4\,\text{meters}

directly behind Sidney and

3\,\text{meters}

directly left of Gordon. Billy makes a paper airplane and throws it to Sidney. Sidney throws the airplane to Gordon, who throws it back to Billy. How far has the paper airplane traveled?

\newline

\_\_\_\_\_

meters

Identify Distances: question_prompt: How far has the paper airplane traveled after being thrown by all three students on the school bus?
Recognize Triangle: Identify the distances between the students. Billy to Sidney is $4$ meters, and Billy to Gordon is $3$ meters.
Apply Pythagorean Theorem: Recognize that the distances form a right triangle with Billy, Sidney, and Gordon at the vertices.
Calculate Distance: Use the Pythagorean Theorem to find the distance from Sidney to Gordon. $a^2 + b^2 = c^2$ , where $a$ is $3$ meters, $b$ is $4$ meters, and $c$ is the distance from Sidney to Gordon.
Simplify Equation: Plug in the values: $3^2 + 4^2 = c^2$ , which simplifies to $9 + 16 = c^2$ .
Find Square Root: Add the values: $9 + 16 = 25$ , so $c^2 = 25$ .
Add Distances: Take the square root of both sides to find $c$ : $\sqrt{c^2} = \sqrt{25}$ , which means $c = 5$ meters.
Calculate Total Distance: Add up the total distance the paper airplane traveled: $4$ meters (Billy to Sidney) + $5$ meters (Sidney to Gordon) + $3$ meters (Gordon to Billy).
Calculate Total Distance: Add up the total distance the paper airplane traveled: $4$ meters (Billy to Sidney) + $5$ meters (Sidney to Gordon) + $3$ meters (Gordon to Billy). Calculate the total distance: $4 + 5 + 3 = 12$ meters.

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