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Beth ran the width of a field, a distance of $35$ yards. Then she ran the length of the field, a distance of $84$ yards. Finally, she ran diagonally across it to get back to her starting point. How far did Beth run? $\newline$ $\_\_\_\_$ yards

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Pythagorean theorem

Full solution

Q. Beth ran the width of a field, a distance of

35

yards. Then she ran the length of the field, a distance of

84

yards. Finally, she ran diagonally across it to get back to her starting point. How far did Beth run?

\newline

\_\_\_\_

yards

Calculate Diagonal Length: question_prompt: How far did Beth run diagonally across the field?
Apply Pythagorean Theorem: Beth ran $35$ yards wide and $84$ yards long, so we need to find the diagonal using the Pythagorean theorem.
Plug in Values: The Pythagorean theorem is $a^2 + b^2 = c^2$ , where $a$ and $b$ are the legs of the right triangle and $c$ is the hypotenuse (the diagonal we're looking for).
Calculate Squares: Plug in the values: $35^2 + 84^2 = c^2$ .
Add Squares: Calculate the squares: $1225 + 7056 = c^2$ .
Find Square Root: Add the squares: $1225 + 7056 = 8281$ .
Calculate Diagonal: Take the square root of $8281$ to find $c$ : $\sqrt{8281} = c$ .
Calculate Diagonal: Take the square root of $8281$ to find $c$ : $\sqrt{8281} = c$ . Calculate the square root: $c = 91$ .

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