Задание 56. A. Заполните таблицу, используя данные рисунка.

Разберем первую таблицу. В треугольнике ABC, MN - средняя линия, параллельная стороне AC. Значит MN = 1/2 * AC. BM = MA, BN = NC.

1) AB = 8, BC = 16, AC = 12. BM = AB/2 = 8/2 = 4. BN = BC/2 = 16/2 = 8. MN = AC/2 = 12/2 = 6. \(P_{AMNB} = AM + MN + NB + BA = 4 + 6 + 8 + 8 = 26\). \(P_{ABC} = AB + BC + CA = 8 + 16 + 12 = 36\)
2) BM = 10, BN = 4, MN = 8. AB = 2 * BM = 2 * 10 = 20. BC = 2 * BN = 2 * 4 = 8. AC = 2 * MN = 2 * 8 = 16.
3) BC = 28, AC = 16, BN = 11. AB = 2 * 11 = 22.
4) AB = 14, AC = 6, MN = 5. AC = 2 * MN = 2 * 5 = 10
5) AB = 12, MN = 7, BN = 9. AC = 2 * MN = 2 * 7 = 14

Ответ:

| | AB | BC | AC | BM | BN | MN | \(P_{AMNB}\) | \(P_{ABC}\) |
|---|-----|-----|-----|-----|-----|-----|----------------|--------------|
| 1 | 8 | 16 | 12 | 4 | 8 | 6 | 26 | 36 |
| 2 | 20 | 8 | 16 | 10 | 4 | 8 | - | - |
| 3 | 22 | 28 | 16 | - | 11 | - | - | - |
| 4 | 14 | - | 6 | - | 5 | - | - | - |
| 5 | 12 | - | 14 | - | 9 | 7 | - | - |