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Adele takes a sheet of paper and cuts from one corner to the opposite corner, making two triangles. If the piece of paper is $9$ inches long and $12$ inches wide, how long is the diagonal cut that Adele made? $\newline$ $\_\_\_\_\_$ inches

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Pythagorean theorem: word problems

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Q. Adele takes a sheet of paper and cuts from one corner to the opposite corner, making two triangles. If the piece of paper is

9

inches long and

12

inches wide, how long is the diagonal cut that Adele made?

\newline

\_\_\_\_\_

inches

Recognize Rectangle Shape: Recognize the paper forms a rectangle and the diagonal cut is the hypotenuse of a right triangle with sides $9$ inches and $12$ inches.
Apply Pythagorean Theorem: Use the Pythagorean Theorem, which is $a^2 + b^2 = c^2$ , where $c$ is the hypotenuse and $a$ and $b$ are the other two sides.
Plug in Side Lengths: Plug in the lengths of the sides into the theorem: $9^2 + 12^2 = c^2$ .
Calculate Squares: Calculate the squares: $9^2 = 81$ and $12^2 = 144$ .
Add Squares: Add the squares together: $81 + 144 = 225$ .
Solve for Hypotenize: Solve for $c$ by taking the square root of $225$ : $\sqrt{225} = c$ .
Calculate Square Root: Calculate the square root: $\sqrt{225} = 15$ .

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