700. In this triangle, we connect the midpoints of the sides; in the new triangle obtained, we do the same; and so on. Without performing calculations: a) what sequence do the perimeters of the successive triangles form; b) the areas of these triangles?
700. An infinite series of similar triangles is obtained, the sides of which are in the ratio $1: \frac{1}{2}: \frac{1}{4}$ and so on. Therefore, infinitely decreasing geometric progressions will be obtained with common ratios a) $\frac{1}{2}$, b) $\frac{1}{4}$.