When you get to the point where the width is larger than the length, you can stop because you have exhausted all the possibilities. The greatest area will be the rectangle that is closer in to a square than any of the others.
So, if k/9=3/9, then k=3, because it is a variable substituting 3. :D Hope I could help!
You basically use the formula height*base/2 to find the area of the triangle. For instance, let's say a is your chosen base, which has a length of 7. You then use the pythagorean theorem of the right triangle (which is formed by splitting the triangle in half), which is a^2+b^2=c^2, and you substitute half your base for a and the other length (8) for c, which is the hypotenuse of the triangle. Note how this is all being done to find "b", which is the height of the triangle, which will then help you substitute all of your known values into the area formula of a triangle to answer your question. I'm not sure if b=141 degrees would have an impact on this question, but I hope this helped you in some way.
Yes it will. For every one hour, the train travels 170 miles. That’s the rate of change/ the ratio-> 1:170
The lateral surface area of a cylinder is just the long side connecting the bases, whereas the total surface area includes both the lateral surface area and area of the two circular bases.

(Imagine a rectangle with the circumfrence of the base as one side and the height as the other being folded around)

(Plus the area of two circles)
The literal difference between surface areas would be the two bases 2πr² if you need that.