Answer:
x = 27
Step-by-step explanation:
BR is parallel to QC therefore ΔBDR and ΔQDC are similar.
The sides are in proportion:
[tex]\dfrac{BD}{QD}=\dfrac{RD}{CD}[/tex]
We have
BD = 26 + 39 = 65
QD = 39
RD = 18 + x
CD = x
Substitute:
[tex]\dfrac{65}{39}=\dfrac{18+x}{x}[/tex] cross multiply
[tex]65x=39(18+x)[/tex] use distributive property
[tex]65x=(39)(18)+39x[/tex] subtract 39x from both sides
[tex]26x=702[/tex] divide both sides by 26
[tex]\boxed{x=27}[/tex]
