So I attempted this problem and I'm very sure I'm doing it right but I keep getting it wrong as my answer choice is not even one of the answer choices listed. There is a picture that goes with the problem that I have attached.
Question: The picture below shows the dimensions of a soccer field. Let x be the distance from the northwest corner to the center of the eastern side and let y be the distance from the northwest corner to the southeast corner. To the nearest meter, what is y – x?
So what I did was I drew out the triangles, the smaller one would have a horizontal side length of 90 m and a vertical side length of 40 m so by the pythagorean theorem, the x value (the hypotenuse) would be 98.49 m. I did the same with the larger triangle that had side lengths of 120 m and 80 m giving me a y of 144.22 m. Calculating y - x results in 45.73 m rounded to 46 m which is not an answer choice. The correct answer choice is actually A: 18 m. I'm not sure if the answer key is wrong or if I'm doing the problem wrong.
First, we find $x$ by Pythagoras. The legs of the right triangle are $120$ and $40.$ Therefore, $x = \sqrt{120^{2} + 40^{2}} = 40\sqrt{10}.$
Next, we find $y,$ also using Pythagoras. The legs of this triangle are $120$ and $80.$ We have that $y = \sqrt{120^{2} + 80^{2}} = 40\sqrt{13}.$
We solve and get $y - x = 40\sqrt{10} - 40\sqrt{13},$ which is closest to $\boxed{\text{(A)}18\text{m}}.$