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Leah's rectangular bedroom is $12$ feet by $9$ feet. What is the diagonal distance from one corner to the opposite corner? $\newline$ $\_\_\_\_$ feet

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Pythagorean theorem: word problems

Full solution

Q. Leah's rectangular bedroom is

12

feet by

9

feet. What is the diagonal distance from one corner to the opposite corner?

\newline

\_\_\_\_

feet

Identify dimensions: Step $1$ : Identify the dimensions of the bedroom. $\newline$ Leah's bedroom is $12$ feet long and $9$ feet wide. We need to find the diagonal, which acts as the hypotenuse in a right triangle formed by the length and width.
Apply Pythagorean Theorem: Step $2$ : Apply the Pythagorean Theorem. $\newline$ Using the formula $a^2 + b^2 = c^2$ , where $a$ and $b$ are the legs and $c$ is the hypotenuse: $\newline$ $12^2 + 9^2 = c^2$
Calculate squares: Step $3$ : Calculate the squares of the legs. $\newline$ $12^2 = 144$ $\newline$ $9^2 = 81$ $\newline$ Adding these gives $144 + 81 = 225$
Solve for hypotenuse: Step $4$ : Solve for the hypotenuse $c$ . $\newline$ $c^2 = 225$ $\newline$ Taking the square root of both sides, $c = \sqrt{225}$ $\newline$ $c = 15$

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