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Rosanne takes a piece of plywood that is $12$ inches long and uses a table saw to make a $20$ -inch cut from corner to opposite corner. What was the width of the piece of plywood? $\newline$ _____ inches

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Pythagorean theorem: word problems

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Q. Rosanne takes a piece of plywood that is

12

inches long and uses a table saw to make a

20

-inch cut from corner to opposite corner. What was the width of the piece of plywood?

\newline

_____ inches

Identify Dimensions and Setup: Identify the known dimensions and the problem setup. $\newline$ Rosanne has a piece of plywood $12$ inches long. She makes a diagonal cut measuring $20$ inches. We need to find the width of the plywood.
Equation Using Pythagorean Theorem: Set up the equation using the Pythagorean Theorem. $\newline$ The diagonal ( $20$ inches) acts as the hypotenuse, and the known side (length) is $12$ inches. Let w be the width. $\newline$ Using the Pythagorean Theorem: $12^2 + w^2 = 20^2$ .
Plug in Values and Simplify: Plug in the values and simplify. $\newline$ $12^2 = 144$ , $\newline$ $20^2 = 400$ , $\newline$ So, $144 + w^2 = 400$ .
Solve for Width: Solve for w^ $2$ . $\newline$ Subtract $144$ from both sides: $w^2 = 400 - 144$ , $\newline$ $w^2 = 256$ .
Find Width Value: Find the value of w. $\newline$ Take the square root of both sides: $w = \sqrt{256}$ , $\newline$ $w = 16$ inches.

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