what is the length of the hypotenuse? if necessary, round to the nearest tenth.\n c = \\boxed{} kilometers

Explanation:

Step1: Identify the formula

For a right - triangle, we use the Pythagorean theorem, which is (a^{2}+b^{2}=c^{2}), where (a) and (b) are the legs of the right - triangle and (c) is the hypotenuse. Here, (a = 5) km and (b=12) km.

Step2: Substitute the values into the formula

Substitute (a = 5) and (b = 12) into the formula (a^{2}+b^{2}=c^{2}). We get (5^{2}+12^{2}=c^{2}). Calculate (5^{2}=25) and (12^{2}=144). Then (25 + 144=c^{2}), so (169=c^{2}).

Step3: Solve for (c)

Take the square root of both sides. Since (c) represents the length of a side of a triangle, we take the positive square root. So (c=\sqrt{169}=13).

Answer:

13