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The ratio between the areas of two triangles

Given is a triangle whose area is S . Each side is extended by a factor p multiplied by its length, to obtain a new triangle, .. The applet allows to investigate the ratio between the areas of the two triangles. The applet permits one to drag the vertices A and C, and thus to change the size of the original triangle. In addition, a ruler for p allows its value to be changed in the range .