Question

In triangle ABC, DE || BC such that \(\frac{AD}{DB} = \frac{4}{x-4}\) and \(\frac{AE}{EC} = \frac{8}{3x-19}\), then the value of x is:

• A. 9
• B. 10
• C. 11
• D. 12

Answer 1

The Correct Option is C

Since \(DE || BC\), we use the property of proportionality. \[ \frac{AD}{DB} = \frac{AE}{EC} \] We are given: \[ \frac{4}{x - 4} = \frac{8}{3x - 19} \] Cross-multiply the equation: \[ 4(3x - 19) = 8(x - 4) \] Solve the equation: \[ 12x - 76 = 8x - 32 \quad \Rightarrow \quad 12x - 8x = 76 - 32 \quad \Rightarrow \quad 4x = 44 \quad \Rightarrow \quad x = 11 \]
Correct Answer:11