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An envelope measures $9$ centimeters by $40$ centimeters. A pencil is placed in the envelope at a diagonal. What is the maximum possible length of the pencil? $\newline$ _____ centimeters

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Pythagorean theorem

Full solution

Q. An envelope measures

9

centimeters by

40

centimeters. A pencil is placed in the envelope at a diagonal. What is the maximum possible length of the pencil?

\newline

_____ centimeters

Form Right Triangle: The envelope and the pencil form a right triangle, with the envelope's length and width as the legs, and the pencil as the hypotenuse.
Use Pythagorean Theorem: Using the Pythagorean Theorem: $a^2 + b^2 = c^2$ , where $a$ and $b$ are the legs, and $c$ is the hypotenuse.
Plug in Dimensions: Plug in the envelope's dimensions for $a$ and $b$ : $9^2 + 40^2 = c^2$ .
Calculate Squares: Calculate the squares: $81 + 1600 = c^2$ .
Add Squares: Add the squares: $81 + 1600 = 1681$ .
Solve for Hypotenize: Solve for $c$ by taking the square root of $1681$ : $c = \sqrt{1681}$ .
Calculate Square Root: Calculate the square root: $c = \sqrt{41}$ .

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