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Then they both will have the same perimeter
You cannot. For a given area, an equilateral triangle will have the smallest perimeter but that perimeter can be increased - without limit - without increasing the area.
You square-root the area
When you are buying a house you will want to know how much you land you have (area) and you will also want know how much fencing you need for you garden (perimeter).
Not exactly. If I know the side lengths, I can still find the perimeter