[tex]\bold{\bar{AC}=12}[/tex]
The correct answer is option (D)
What are similar triangles?
"Two triangles are said to be similar if the corresponding sides are in proportion and the corresponding angles are equal."
For given question,
ΔABC is similar to ΔLMN
So, the sides of these triangles must be in proportion.
[tex]\frac{AB}{LM} =\frac{BC}{MN}= \frac{AC}{LN}[/tex]
Consider,
[tex]\Rightarrow \frac{AB}{LM}= \frac{AC}{LN} \\\\\Rightarrow \frac{5}{10} =\frac{x+5}{3x+3}\\\\ \Rightarrow \frac{1}{2} =\frac{x+5}{3x+3}\\\\ \Rightarrow 3x+3=2\times (x+5)\\\\\Rightarrow 3x + 3 =2x+10\\\\\Rightarrow 3x-2x=10-3\\\\\Rightarrow x=7[/tex]
Now, we find the length of the side AC.
[tex]\bar{AC}\\=x+5\\\\=7+5\\\\=12~units[/tex]
Therefore, [tex]\bold{\bar{AC}=12}[/tex]
The correct answer is option (D)
Learn more about similar triangle here:
https://brainly.com/question/25882965
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