Plots of land between two roads are laid out according to the boundaries shown. the boundaries between the two roads are parallel. what is the length of plot 3 along chesire road? picture attached. you

Check out the image below. I marked your diagram adding a red marker to indicate what we want to solve for. Call this x.

The ratio of the two road lengths from Shelby to Chesire road are the same due to the parallel lines being there. They divide up the figures in a proportional manner.

Along plot 1, we have the lengths 40 and 48 which forms the fraction 40/48. Note how I started at the top and moved down (started at Chesire; moved to Shelby)

Along plot 3, we have the lengths x and 65. Again the order is from top to bottom. It's important to keep this order so you can match the terms. This forms the fraction x/65

Equate the two fractions, cross multiply, then isolate x

40/48 = x/65

40*65 = 48*x ..... cross multiply

2600 = 48x

48x = 2600

48x/48 = 2600/48 .... divide both sides by 48

x = 54.167 which is approximate

note: The answer is rounded to three decimal places. The decimal approximation has the '6's go on forever. If you need the exact length in terms of a fraction, then reduce 2600/48 to get 325/6 (divide both parts by the GCF 8). The improper fraction 325/6 converts to the mixed number 54 & 1/6. So we have 54 whole yards plus one-sixth of a yard (aka half a foot = 6 inches). So this is equivalent to 54 yards + 6 inches. Personally I find the mixture of units to be confusing; however, I've noticed that football games use this notation when talking about how far it is to the line to gain (or similar). So maybe it will make more sense this way.

y=mx+b is the final answer!   : )