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Tara's rectangular bedroom is $4\,\text{meters}$ by $3\,\text{meters}$ . What is the diagonal distance from one corner to the opposite corner? $\newline$ $\_\_\_\_\_$ meters

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Pythagorean theorem: word problems

Full solution

Q. Tara's rectangular bedroom is

4\,\text{meters}

by

3\,\text{meters}

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

\newline

\_\_\_\_\_

meters

Identify Dimensions and Diagonal: Identify the dimensions of the bedroom and the diagonal as the hypotenuse of a right triangle. $\newline$ Length: $4\,\text{m}$ , Width: $3\,\text{m}$ , Diagonal (hypotenuse): $x\,\text{m}$ .
Apply Pythagorean Theorem: Apply the Pythagorean Theorem: $(\text{Leg1})^2 + (\text{Leg2})^2 = (\text{Hypotenuse})^2$ . Using the dimensions: $4^2 + 3^2 = x^2$ .
Calculate Squares of Legs: Calculate the squares of the legs. $\newline$ $4^2 = 16$ , $3^2 = 9$ . $\newline$ $16 + 9 = x^2$ .
Add Results for $x^2$ : Add the results to find $x^2$ . $\newline$ $16 + 9 = 25$ . $\newline$ $x^2 = 25$ .
Find Value of x: Find the value of $x$ by taking the square root of $25$ . $\sqrt{25} = 5$ . $x = 5$ .

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