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Greg is building a slide for his kids. The ladder is $3\,\text{meters}$ tall and the slide is $5\,\text{meters}$ long. What is the distance between the ladder and the bottom of the slide? $\newline$ $\_\_\_\_\_$ meters

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Pythagorean theorem: word problems

Full solution

Q. Greg is building a slide for his kids. The ladder is

3\,\text{meters}

tall and the slide is

5\,\text{meters}

long. What is the distance between the ladder and the bottom of the slide?

\newline

\_\_\_\_\_

meters

Identify Dimensions and Relationship: Identify the dimensions given and the relationship between them. $\newline$ Ladder height (vertical leg): $3$ meters, $\newline$ Slide length (hypotenuse): $5$ meters, $\newline$ Distance between ladder and bottom of the slide (horizontal leg): $x$ meters. $\newline$ Using the Pythagorean Theorem: $(\text{Vertical leg})^2 + (\text{Horizontal leg})^2 = (\text{Hypotenuse})^2$ .
Plug in Known Values: Plug in the known values into the Pythagorean Theorem. $\newline$ $3^2 + x^2 = 5^2$ , $\newline$ $9 + x^2 = 25$ .
Solve for $x^2$ : Solve for $x^2$ . $\newline$ $x^2 = 25 - 9$ , $\newline$ $x^2 = 16$ .
Find $x$ : Find $x$ by taking the square root of $x^2$ . $\sqrt{16} = 4$ , $x = 4$ meters.

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