Given:
[tex]\Delta LMN\sim \Delta LRS[/tex]
To find:
The value of x.
Solution:
We have,
[tex]\Delta LMN\sim \Delta LRS[/tex]
We know that the corresponding sides of similar triangles are proportional. So,
[tex]\dfrac{LM}{LR}=\dfrac{LN}{LS}[/tex]
[tex]\dfrac{18}{2x-18}=\dfrac{30}{10}[/tex]
[tex]\dfrac{18}{2x-18}=3[/tex]
[tex]18=3(2x-18)[/tex]
Using distributive property, we get
[tex]18=3(2x)-3(18)[/tex]
[tex]18=6x-54[/tex]
[tex]18+54=6x[/tex]
[tex]72=6x[/tex]
Divide both sides by 6.
[tex]\dfrac{72}{6}=x[/tex]
[tex]12=x[/tex]
Therefore, the correct option is A.
