Answer/Step-by-step explanation:
∆ABC is similar to ∆CDE. Therefore, the ratio of their corresponding sides are proportional.
This,
[tex] \frac{DE}{AB} = \frac{DC}{AC} [/tex]
[tex] \frac{4}{3} = \frac{x + 3}{x + 1} [/tex]
Solve for x
[tex] 4(x + 1) = 3(x + 3) [/tex]
[tex] 4x + 4 = 3x + 9 [/tex]
[tex] 4x + 4 - 4 = 3x + 9 - 4[/tex]
[tex] 4x = 3x + 5 [/tex]
[tex] 4x - 3x = 3x + 5 - 3x [/tex]
[tex] x = 5 [/tex]
Use the value of x to find AC and DC
[tex] AC = x + 1 = 5 + 1 = 6 [/tex]
[tex] DC = x + 3 = 5 + 3 = 8 [/tex]
