Answer:
Option D is correct.
Value of x is, 10 units.
Step-by-step explanation:
Triangle Proportionality theorem states that if a line parallel to one side of a triangle intersects the other two sides of a triangle, then the line divide these two sides proportionality.
Given that: ![\overline{PQ} || \overline{BC}](https://tex.z-dn.net/?f=%5Coverline%7BPQ%7D%20%7C%7C%20%5Coverline%7BBC%7D)
From the given figure, we have;
AP = 3 units , PB = 6 units , QC = 20 units and AQ = x units.
then, by triangle proportionality theorem;
![\frac{AP}{PB} =\frac{AQ}{QC}](https://tex.z-dn.net/?f=%5Cfrac%7BAP%7D%7BPB%7D%20%3D%5Cfrac%7BAQ%7D%7BQC%7D)
Substitute the given values, to find the value of x;
![\frac{3}{6} =\frac{x}{20}](https://tex.z-dn.net/?f=%5Cfrac%7B3%7D%7B6%7D%20%3D%5Cfrac%7Bx%7D%7B20%7D)
By cross multiply we have;
![60 = 6x](https://tex.z-dn.net/?f=60%20%3D%206x)
Divide both sides by 6 we get;
10 = x
Therefore, the value of x is, 10 units