A metre would be the most appropriate unit.
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w = width l = length A =area = wl = 64 l = 2w + 8 wl = w(2w+8) = 64 2w^2 +8w -64 = 0 w^2 + 4w -32 = 0 (w+8)(w-4) = 0 w = 4 wl =4 l = 64 l = 16 length = 16 feet
The barn will still be 50 feet wide by 80 feet long. The scale does not affect the original object, only its image (or model).
Assuming all of the 4 people worked at the same pace originally, it would take two people 6 days.
If the scale is 1 to 16, then each dimension in the real world is 16 times its size on the drawing, and its size on the drawing is 1/16 of its real size. The barn must be drawn 2-ft high on the plans.
daily life examples for area and perimeter: 1) Fencing off an area to plot a crop. Since fences cost money for a given area you would want to minimize the perimeter. 2) Planning the construction of a house. Since you have to pour a concrete foundation, within the housing constraints you want to maximize the area within the constraints which are related to the perimeter (like you can only get so close to a neighbor's house, etc.) 3) Building a barn with box stalls for horses. You would again like to minimize the building material used and build for the largest area given the amount of building material that you have planned for. This one I know, I did the computations and architecture for a barn filled with box stalls. 4) Wood. If you buy wood for a construction project and you can choose between 8 inch wide wood that is 60 feet long and thus has an area of 40 square feet or 12 inch thick wood that is 40 feet long and thus is 40 square feet, there are many considerations. But the width and length of the different width boards while the same area have a different price based on the perimeter. 5) Building a swimming pool. You want to maximize the area within constraints of property and minimize the amount of digging and concrete, etc. that goes into the project. Yet the perimeter also defines length that is used for swimming races.