Question

the figure represents a swing set. the supports on each side of the swing set are constructed from 12 - foot poles connected at their midpoints. the distance between the bases of the two poles is 5 feet. what is the length of each brace? feet

Explanation:

Step1: Determine the height from mid - point

Since the poles are 12 feet long and connected at mid - points, the height from the mid - point to the ground for each pole is $\frac{12}{2}=6$ feet.

Step2: Apply the Pythagorean theorem

The distance between the bases of the poles is 5 feet, and we consider a right - triangle formed by half of the distance between the bases (2.5 feet) and the height from the mid - point to the ground (6 feet). Let the length of the brace be $c$. According to the Pythagorean theorem $c=\sqrt{2.5^{2}+6^{2}}$.
First, calculate $2.5^{2}=6.25$ and $6^{2} = 36$. Then $2.5^{2}+6^{2}=6.25 + 36=42.25$.
So, $c=\sqrt{42.25}=6.5$ feet.

Answer:

6.5