Question

Se dau punctele colineare A, B, C, D in aceasta ordine astfel ca 4 × AB + 5 × AD= 9 × AC si BD= 18 cm. Aflati BC si CD
Va rog ajutati-ma repede dau coronita ​

Answer 1

Explicație pas cu pas:

A ...x... B ...y... C ...z... D

notez AB = x; BC = y; CD = z

AD = AB + BD = x + 18

AC = x + y

BD = y + z = 18

4 × AB + 5 × AD = 9 × AC

4x + 5(x+18) = 9(x+y)

4x + 5x + 90 = 9x + 9y

9x + 90 = 9x + 9y

9y = 90 => y = 10 => BC = 10 cm

CD = BD-BC = 18-10 => CD = 8 cm