Question

На рисунке изображена фигура, состоящая из пяти маленьких треугольников. Нарисуй фигуру, состоящую из восьми маленьких треугольников, так. чтобы её периметр был как можно меньше.

Answer 1

Drawing a Figure with Eight Small Triangles

To create a figure consisting of eight small triangles with the minimum possible perimeter, we can arrange the triangles in a way that minimizes the total length of their sides. One possible arrangement is shown below:

     /\
    /__\
   /\  /\
  /__\/__\
 /\      /\
/__\    /__\

In this arrangement, the eight small triangles are arranged in a rectangular shape, with four triangles on the top row and four triangles on the bottom row. The sides of the triangles are shared, resulting in a figure with a total of eight triangles.

Minimizing the Perimeter

To minimize the perimeter of the figure, we need to minimize the length of the sides of the small triangles. In the arrangement shown above, each small triangle shares a side with two neighboring triangles. This means that the total length of the shared sides is minimized, resulting in a smaller overall perimeter compared to other arrangements.

By arranging the triangles in a rectangular shape, we can ensure that the shared sides are as short as possible. This is because the sides of a rectangle are perpendicular to each other, allowing for efficient use of space and minimizing the total length of the shared sides.

Conclusion

By arranging eight small triangles in a rectangular shape, we can create a figure with the minimum possible perimeter. The arrangement shown above demonstrates one possible configuration that achieves this goal.