Answer: X = 27
Step-by-step explanation: The diagram shows two triangles with one triangle cut out from the other. A careful observation would reveal triangle BDR and triangle QDC.
Since line QC is parallel to line BR, that makes triangle QDC similar to triangle BDR. Also the ratio of lines QD and BQ is the same as the ratio of lines CD and RD. The same applies to lines QC and BR.
Therefore,
QD/BQ = CD/RC
Alternatively we can use the ratios,
QD/BD = CD/RD
Using the first ratios, we have
QD/BQ = CD/RC
39/26 = X/18
3/2 = X/18 {the left hand side has been reduced to it's simplest form}
If we cross multiply, we now arrive at
3 × 18 = 2X
54 = 2X
Divide both sides of the equation by 2
27 = X
