Найдите х, у. 8 B DE AC 10 E 7.2 7,8 16 C

Так как DE || AC, треугольники BDE и BAC подобны. Тогда:

$$\frac{BD}{BA} = \frac{BE}{BC} = \frac{DE}{AC}$$

$$\frac{x}{x+7.2} = \frac{y}{y+7.8} = \frac{10}{16}$$

$$\frac{x}{x+7.2} = \frac{5}{8}$$

$$8x = 5(x+7.2)$$

$$8x = 5x + 36$$

$$3x = 36$$

$$x = 12$$

$$\frac{y}{y+7.8} = \frac{5}{8}$$

$$8y = 5(y+7.8)$$

$$8y = 5y + 39$$

$$3y = 39$$

$$y = 13$$

Ответ: x = 12, y = 13