Question

in georgetown, the library is 3 kilometers south of the courthouse and 4 kilometers west of the community swimming pool. if a bird flew directly from the courthouse to the library, then from the library to the swimming pool, and then from the swimming pool back to the courthouse, what would be the total distance flown? if necessary, round to the nearest tenth. kilometers

Explanation:

Step1: Find the distance from courthouse to swimming pool

The distance from courthouse to library is \(3\) km (south - north direction) and library to swimming pool is \(4\) km (west - east direction). These two paths form the two legs of a right - triangle. By the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), where \(a = 3\), \(b = 4\). Then \(c=\sqrt{3^{2}+4^{2}}=\sqrt{9 + 16}=\sqrt{25}=5\) km (distance from courthouse to swimming pool).

Step2: Calculate the total distance

The bird's path is courthouse - library (\(d_1=3\) km), library - swimming pool (\(d_2 = 4\) km), swimming pool - courthouse (\(d_3=5\) km). The total distance \(D=d_1 + d_2+d_3\). So \(D=3 + 4+5=12\) km.

Answer:

\(12\)