Question

stop at point b. how far apart are the trains when both are at their first stop? round the answer to the nearest integer. not drawn to scale 65 km 139 km 224 km 275 km

Explanation:

Step1: Identify the triangle type

The triangle formed by points A, Station, and B is a right triangle (since there's a right angle at the Station). So we can use the Pythagorean theorem, which states that for a right triangle with legs \(a\) and \(b\), and hypotenuse \(c\), \(c = \sqrt{a^2 + b^2}\). Here, \(a = 100\) km, \(b = 200\) km, and \(d\) (the distance between A and B) is the hypotenuse.

Step2: Apply the Pythagorean theorem

Substitute \(a = 100\) and \(b = 200\) into the formula: \(d=\sqrt{100^2 + 200^2}\)
First, calculate the squares: \(100^2 = 10000\) and \(200^2 = 40000\)
Then, add them: \(10000 + 40000 = 50000\)
Now, take the square root: \(d=\sqrt{50000}\)
Simplify \(\sqrt{50000}\): \(\sqrt{50000}=\sqrt{10000\times5}=100\sqrt{5}\approx100\times2.236 = 223.6\)

Step3: Round to the nearest integer

\(223.6\) rounded to the nearest integer is \(224\).

Answer:

224 km (corresponding to the option "224 km")