Question

1. what is the value of x?

a 3
b 9
c 15
d 30

Explanation:

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

If a line is parallel to one side of a triangle and intersects the other two sides, then it divides those sides proportionally. So, \(\frac{2x - 8}{5}=\frac{x - 3}{3}\).

Step2: Cross - multiply

Cross - multiplying gives \(3(2x - 8)=5(x - 3)\).
Expanding both sides: \(6x-24 = 5x - 15\).

Step3: Solve for \(x\)

Subtract \(5x\) from both sides: \(6x-5x-24=5x - 5x-15\), which simplifies to \(x-24=-15\).
Add \(24\) to both sides: \(x=-15 + 24\).

Answer:

\(x = 9\), so the answer is B. 9.