It really depends on what your hypothesis is! But I expect a hypotenuse could be more useful in this context. However, knowledge of the hypothesis, hypotenuse even, is not enough to enable you to find the perimeter.
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That depends on what type of triangle is if the side given is equal to the perimeter divided by 3 then it is an equilateral triangle.
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.
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Measure it or use trigonometry if the 'included' angle is given.
It is: perimeter minus hypotenus+base = height Area = 0.5*base*height