10.1 Complete the following statement: A line drawn parallel to one side of a triangle divides the other two sides in .. - NSC Mathematics - Question 10 - 2016 - Paper 2

By the Basic Proportionality Theorem (or Thales's theorem), if a line is drawn parallel to one side of a triangle, it divides the other two sides proportionally. Thus, if DE is drawn parallel to BC, then:

$\frac{AD}{DB} = \frac{AE}{EC}$

To find the value of x, we can use the properties of parallelograms. In parallelograms, opposite sides are equal, thus:

1. From the triangle, we have:

   • PT = QT - QW

   • Substituting the values we get:

   • ( x + 2 = 15 - (x + 4) )

   • Simplifying: ( x + 2 = 15 - x - 4 ) ( x + 2 = 11 - x ) ( 2x = 9 ) ( x = 4.5 )

Hence, the value of x is 4.5.

Using the previously calculated value of x:

• From the problem, we have WR = x, thus WR = 4.5 units.
• In parallelogram TVRW, opposite sides are equal, therefore VR = PT. Since VR = 18 units, we can find the length of PV:
• PV = PT + TV = (x + 2) + (x + 4) = (4.5 + 2) + (4.5 + 4) = 6.5 + 8.5 = 15 units.

Thus, the length of PV is 15 units.