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Polly measured the floor of her storage unit, which is rectangular. It is $14$ feet wide and $50$ feet from one corner to the opposite corner. How long is the storage unit? $\newline$ $\_\_\_\_$ feet

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Pythagorean theorem

Full solution

Q. Polly measured the floor of her storage unit, which is rectangular. It is

14

feet wide and

50

feet from one corner to the opposite corner. How long is the storage unit?

\newline

\_\_\_\_

feet

Identify Triangle: question_prompt: How long is Polly's storage unit?
Use Pythagorean Theorem: Identify the right triangle formed by the width, length, and diagonal of the storage unit.
Plug in Values: Use the Pythagorean Theorem: $a^2 + b^2 = c^2$ , where $a$ is the width, $b$ is the length, and $c$ is the diagonal.
Calculate Squares: Plug in the known values: $14^2 + b^2 = 50^2$ .
Subtract $196$ : Calculate the squares: $196 + b^2 = 2500$ .
Simplify Subtraction: Subtract $196$ from both sides: $b^2 = 2500 - 196$ .
Take Square Root: Simplify the subtraction: $b^2 = 2304$ .
Calculate Square Root: Take the square root of both sides to solve for $b$ : $b = \sqrt{2304}$ .
Calculate Square Root: Take the square root of both sides to solve for $b$ : $b = \sqrt{2304}$ . Calculate the square root: $b = 48$ .

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