Question

emilio is building a slide for his kids. the ladder is 3 meters tall and the slide is 5 meters long. what is the distance between the ladder and the bottom of the slide? meters

Explanation:

Step1: Apply Pythagorean theorem

Let the distance be \(x\). The ladder height (\(a = 3\)m) and the distance (\(x\)) are the legs of a right - triangle, and the slide length (\(c=5\)m) is the hypotenuse. By the Pythagorean theorem \(a^{2}+x^{2}=c^{2}\), so \(x^{2}=c^{2}-a^{2}\).

Step2: Substitute values

Substitute \(a = 3\) and \(c = 5\) into \(x^{2}=c^{2}-a^{2}\). Then \(x^{2}=5^{2}-3^{2}=25 - 9=16\).

Step3: Solve for \(x\)

Take the square root of both sides. Since \(x>0\) (distance), \(x=\sqrt{16}=4\).

Answer:

\(4\)