The ratio between the areas of two triangles

Given is a triangle ABC. Each side is extended by a factor p multiplied by its length, to obtain a new triangle, A’B’C’. The applet allows to investigate the ratio between the area of the new triangle A’B’C’ and the area of the original triangle ABC and specify for which the value of p is the minimal ratio obtained. One can drag the vertices A,B 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 -2<=p<=2.The area ratio of the triangles and the graph describing this ratio as a function of p are shown for each value of p.