Answer:
B. 12
Step-by-step explanation:
✔️Find the value of x
The side lengths of two similar triangles are always proportional.
Given that ∆ABC ~ ∆LMN, therefore:
[tex] \frac{AB}{LM} = \frac{AC}{LN} [/tex]
AB = 5
LM = 10
AC = x + 5
LN = 3x + 3
Plug in the values
[tex] \frac{5}{10} = \frac{x + 5}{3x + 3} [/tex]
Cross multiply
[tex] 5(3x + 3) = 10(x + 5) [/tex]
[tex] 15x + 15 = 10x + 50 [/tex] (distributive property)
Collect like terms
[tex] 15x - 10x = -15 + 50 [/tex]
[tex] 5x = 35 [/tex]
Divide both sides by 5
x = 7
✔️Find AC
AC = x + 5
Plug in the value of x
AC = 7 + 5
AC = 12
