Question

Доно: треугольник АВС подобен треугольник А1В1С1
Найти: x,y,z

Answer 1

Ответ:

$\Delta ABC\sim \Delta A_1B_1C_1\ \ \ \Rightarrow \ \ \ \dfrac{AB}{A_1B_1}=\dfrac{AC}{A_1C_1}=\dfrac{BC}{B_1C_1}=\dfrac{P}{P_1}\\\\\\\dfrac{6}{y}=\dfrac{7}{z}=\dfrac{8}{x}=\dfrac{6+7+8}{105}\\\\\\\dfrac{6}{y}=\dfrac{21}{105}\ \ ,\ \ \ y=\dfrac{6\cdot 105}{21}\ \ ,\ \ \ y=30\\\\\\\dfrac{7}{z}=\dfrac{21}{105}\ \ ,\ \ \ y=\dfrac{7\cdot 105}{21}\ \ ,\ \ \ y=35\\\\\\\dfrac{8}{x}=\dfrac{21}{105}\ \ ,\ \ \ y=\dfrac{8\cdot 105}{21}\ \ ,\ \ \ y=40$