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Rose is building a slide for her kids. The ladder is $8$ feet tall and the slide is $17$ feet long. What is the distance between the ladder and the bottom of the slide? $\newline$ $\_\_\_\_$ feet

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Pythagorean theorem

Full solution

Q. Rose is building a slide for her kids. The ladder is

8

feet tall and the slide is

17

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

\newline

\_\_\_\_

feet

Identify Dimensions: Identify the dimensions given in the problem: the ladder is $8$ feet tall (height), and the slide is $17$ feet long (hypotenuse).
Set up Pythagorean Theorem: Set up the Pythagorean theorem to find the distance (base) between the ladder and the bottom of the slide. Let's call this distance $x$ . The equation is $\text{height}^2 + \text{base}^2 = \text{hypotenuse}^2$ .
Plug in Values: Plug in the known values: $8^2 + x^2 = 17^2$ .
Calculate Squares: Calculate the squares: $64 + x^2 = 289$ .
Isolate $x^2$ : Isolate $x^2$ : $x^2 = 289 - 64$ .
Simplify Equation: Simplify the equation: $x^2 = 225$ .
Solve for x: Solve for x by taking the square root of both sides: $x = \sqrt{225}$ .
Calculate Square Root: Calculate the square root: $x = 15$ .

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