I think this means we have a shape with a perimeter 39cm and we are asked what is the smallest area. It is a rectangle of length 19.5cm and width zero. Or perhaps it should read area 49 cm squared., what is the smallest periimeter. A circle with 49=pi x r2. Then perimeter=pi x 2r
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Area = 49 cm2 so side = sqrt(49) cm = 7 cm and therefore, perimeter = 4*side = 28 cm.
Perimeter = 28 = 4s = 4 x 7 Therefore, each side is 7cm long Area = s x s = 7 x 7 = 49cm squared
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A 9 x 1 rectangle has a perimeter of 20 and an area of 9; A 9.5 x 0.5 rectangle has the same perimeter but an area of 4.75; You can go a long way along this road...
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.