Question

13.
32
2x + 6
60
52.5

Explanation:

Step1: Apply the Basic Proportionality Theorem (Thales' theorem)

The theorem states that if a line is drawn parallel to one side of a triangle, intersecting the other two sides, then it divides those sides proportionally. So, we can set up the proportion: $\frac{32}{60}=\frac{2x + 6}{52.5}$

Step2: Cross - multiply to solve for x

Cross - multiplying gives us $32\times52.5=60\times(2x + 6)$
First, calculate $32\times52.5 = 1680$ and $60\times(2x + 6)=120x+360$
So, the equation becomes $1680 = 120x+360$

Step3: Isolate the variable term

Subtract 360 from both sides: $1680 - 360=120x$
$1320 = 120x$

Step4: Solve for x

Divide both sides by 120: $x=\frac{1320}{120}=11$

Answer:

$x = 11$