Question

In Somerville, the library is 5 kilometers due south of the courthouse and 12 kilometers due west of the community swimming pool. What is the distance between the courthouse and the community swimming pool?

Answer 1

Using the Pythagorean theorem, the distance between the courthouse and the community swimming pool is determined to be 13 kilometers.

Step-by-step explanation:

We can determine the distance between the courthouse and the community swimming pool by visualizing the situation as a right-angled triangle, with the library at the vertex where the right angle is. The courthouse is 5 kilometers to the north (since it is south of the library), and the community swimming pool is 12 kilometers to the east (since it is west of the library). Using the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

So, if we let c represent the distance between the courthouse and the community swimming pool, we have:

c² = 5² + 12²

c² = 25 + 144

c² = 169

√c² = √169

c = 13 kilometers

Therefore, the distance between the courthouse and the community swimming pool is 13 kilometers.