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: [tex]\overline{PQ} || \overline{BC}[/tex]
From the given figure, we have;
AP = 3 units , PB = 6 units , QC = 20 units and AQ = x units.
then, by triangle proportionality theorem;
[tex]\frac{AP}{PB} =\frac{AQ}{QC}[/tex]
Substitute the given values, to find the value of x;
[tex]\frac{3}{6} =\frac{x}{20}[/tex]
By cross multiply we have;
[tex]60 = 6x[/tex]
Divide both sides by 6 we get;
10 = x
Therefore, the value of x is, 10 units
