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Alexandra is going to swim the length of her swimming pool. The width of her pool is $21$ meters and the diagonal distance from one corner to the opposite corner is $29$ meters. How far will Alexandra swim when she swims the length? $\newline$ _____ meters

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Pythagorean theorem

Full solution

Q. Alexandra is going to swim the length of her swimming pool. The width of her pool is

21

meters and the diagonal distance from one corner to the opposite corner is

29

meters. How far will Alexandra swim when she swims the length?

\newline

_____ meters

Identify Parameters: We know the width $21$ meters) and the diagonal $29$ meters) of the pool. We need to find the length.
Apply Pythagorean Theorem: Let's call the length we're looking for ' $l$ '. We can use the Pythagorean Theorem: $\text{width}^2 + \text{length}^2 = \text{diagonal}^2$ .
Substitute Values: Plug in the known values: $21^2 + l^2 = 29^2$ .
Calculate Squares: Calculate the squares: $441 + l^2 = 841$ .
Solve for $l^2$ : Subtract $441$ from both sides to solve for $l^2$ : $l^2 = 841 - 441$ .
Find Square Root: Do the subtraction: $l^2 = 400$ .
Final Calculation: Take the square root of both sides to solve for $l$ : $l = \sqrt{400}$ .
Final Calculation: Take the square root of both sides to solve for $l$ : $l = \sqrt{400}$ . Calculate the square root: $l = 20$ .

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