Question

on the school playground, the slide is 4 meters due west of the tire swing and 3 meters due south of the monkey bars. what is the distance between the tire swing and the monkey bars?
meters
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Explanation:

Step1: Identify the problem type

This is a right - triangle distance problem. The slide's west - east (4 meters west) and south - north (3 meters south) displacements from the monkey bars form the two legs of a right triangle, and the distance between the tire swing (at the slide's position) and the monkey bars is the hypotenuse.

Step2: Apply the Pythagorean theorem

The Pythagorean theorem states that for a right triangle with legs of lengths \(a\) and \(b\) and hypotenuse of length \(c\), \(c=\sqrt{a^{2}+b^{2}}\). Here, \(a = 4\) meters and \(b=3\) meters.

First, calculate \(a^{2}\) and \(b^{2}\):
\(a^{2}=4^{2}=16\)
\(b^{2}=3^{2} = 9\)

Then, find the sum of \(a^{2}\) and \(b^{2}\):
\(a^{2}+b^{2}=16 + 9=25\)

Finally, find the square root of the sum:
\(c=\sqrt{25}=5\)

Answer:

5