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:
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:
Updated On: Oct 27, 2025
- 9
- 10
- 11
- 12
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The Correct Option is C
Solution and Explanation
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
Correct Answer:11
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