ΔDCQ and ΔDRB are similar triangles thus the corresponding sides of the triangles have the same proportion.
Make a comparison of the corresponding sides
[tex] \frac{DC}{DR}= \frac{DQ}{DB} [/tex]
plug in the numbers to the comparison above
[tex] \frac{DC}{DR}= \frac{DQ}{DB} [/tex]
[tex]\frac{x}{x+18}= \frac{39}{39 + 26}[/tex]
simplify the equation
[tex]\frac{x}{x+18}= \frac{39}{39 + 26}[/tex]
[tex] \frac{x}{x+18}= \frac{39}{65} [/tex]
simplify 39 and 65 by dividing them by 13
[tex] \frac{x}{x+18}= \frac{3}{5} [/tex]
Do cross multiplication
[tex] \frac{x}{x+18}= \frac{3}{5} [/tex]
[tex]5x=3(x+18)[/tex]
Solve the equation
5x = 3(x + 18)
5x = 3x + 54
5x - 3x = 54
2x = 54
x = 54/2
x = 27
The value of x
[tex]\boxed{\boxed{x=27}}[/tex]
