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An envelope measures $8$ inches by $6$ inches. A pencil is placed in the envelope at a diagonal. What is the maximum possible length of the pencil? $\newline$ $\_\_\_\_$ inches

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Pythagorean theorem: word problems

Full solution

Q. An envelope measures

8

inches by

6

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

\newline

\_\_\_\_

inches

Identify dimensions and diagonal: Step $1$ : Identify the dimensions of the envelope and the diagonal. $\newline$ The envelope has a length of $8$ inches and a width of $6$ inches. The diagonal, where the pencil lies, is the longest possible line that can be drawn within the rectangle formed by the envelope.
Apply Pythagorean Theorem: Step $2$ : Apply the Pythagorean Theorem to find the diagonal. $\newline$ Using the formula for the Pythagorean Theorem, which is $a^2 + b^2 = c^2$ , where $a$ and $b$ are the lengths of the legs and $c$ is the length of the hypotenuse (diagonal in this case). $\newline$ Calculation: $8^2 + 6^2 = c^2$ $\newline$ $64 + 36 = c^2$ $\newline$ $100 = c^2$
Solve for diagonal: Step $3$ : Solve for the diagonal, $c$ . To find the length of the diagonal, take the square root of $100$ . $\sqrt{100} = 10$ So, the diagonal is $10$ inches long.

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