• Hm. Here's one way to do it. Can choose one of the sides arbitrarily, as it doesn't affect the answer. So put side a on the x-axis with its center at x=0 and imagine triangles with a given area. a is the base, so all such triangles must have the same height. Choose point A at height h and x coordinate x. The area of the triangles are constant. Find b and c in terms of h, x and a. so find the minimum of abc(a+b+c) in terms of x. sqrt and divide by the area of the triangle at that value of x.

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