Russell Gossman is training for the Olympics. He wants to know the distance across Lake Royal, so he can write in his training logbook how far he rows each day. If from one point on the shore to one side of the lake is 13 km and from the same point to another side of the lake is 16 km, what is the approximate length in km of the lake?

Oh the possible answers are

9
18
44
87

I think it is 18 but i'm not sure.

Units of measurements for answers?

Well if it is km.s then yes it is 18.

To find the approximate length of Lake Royal, you need to use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

In this case, you can treat the distance from one point on the shore to one side of the lake (13 km) as one side of a right triangle, and the distance from the same point to another side of the lake (16 km) as the other side of the triangle. The length of the lake will be the hypotenuse of the triangle.

Here's how you can calculate the approximate length of Lake Royal:

Step 1: Square the two given distances:
13 km squared = 169 km^2
16 km squared = 256 km^2

Step 2: Add the squared distances:
169 km^2 + 256 km^2 = 425 km^2

Step 3: Take the square root of the sum to find the length of the lake:
√425 km^2 ≈ 20.62 km

Therefore, the approximate length of Lake Royal is approximately 20.62 km.