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Brooke takes a sheet of paper and makes a diagonal cut from one corner to the opposite corner, making two triangles. The cut she makes is $20$ centimeters long and the width of the paper is $12$ centimeters. What is the paper's length? $\newline$ $\_\_\_\_\_$ centimeters

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Pythagorean theorem: word problems

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Q. Brooke takes a sheet of paper and makes a diagonal cut from one corner to the opposite corner, making two triangles. The cut she makes is

20

centimeters long and the width of the paper is

12

centimeters. What is the paper's length?

\newline

\_\_\_\_\_

centimeters

Identify Problem: Identify the problem as a right triangle problem where the diagonal is the hypotenuse and the width is one leg. We need to find the other leg, which is the length of the paper. $\newline$ Calculation: Use the Pythagorean theorem, $a^2 + b^2 = c^2$ , where $c$ is the hypotenuse ( $20\,\text{cm}$ ), $b$ is the width ( $12\,\text{cm}$ ), and $a$ is the length we need to find.
Calculate Using Pythagorean Theorem: Plug in the known values into the Pythagorean theorem. $\newline$ Calculation: $12^2 + a^2 = 20^2$
Plug in Known Values: Simplify the equation to find $a^2$ . $\newline$ Calculation: $144 + a^2 = 400$
Simplify Equation: Solve for $a^2$ . $\newline$ Calculation: $a^2 = 400 - 144$ $\newline$ $a^2 = 256$
Solve for $a^2$ : Find the value of $a$ by taking the square root of $a^2$ . $\newline$ Calculation: $a = \sqrt{256}$ $\newline$ $a = 16$

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