Since QC and BR are parallel, triangles CDQ and BDR are similar.
This means that corresponding sides are in proportion, so we have
[tex] BD \div QD = RD \div CD [/tex]
Substituting numbers, we have
[tex] 26+39 \div 39 = 18+x \div x \iff \dfrac{65}{39} = \dfrac{18+x}{x} [/tex]
Multiply both sides by [tex] 39x [/tex]
[tex] 65x = 39(18+x) [/tex]
Expand right hand side:
[tex] 65x = 702 + 39x [/tex]
Subtract 39x from both sides:
[tex] 26x = 702 [/tex]
Divide both sides by 26
[tex] x = \dfrac{702}{26} = 27 [/tex]
