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
Show Solution
Verified By Collegedunia
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
Was this answer helpful?
0
0
Top Bihar Class X Board Mathematics Questions
- If 5th term of an A.P. is 11 and common difference is 2 then what is its first term ?
- The sum of an A.P. with n terms is \(n^2 + 2n + 1\) then its 6th term is
- Which of the following is in an A.P. ?
- Which of the following is not in an A.P. ?
- The sum of first 20 terms of the A.P. 1, 4, 7, 10, ... is
View More Questions
Top Bihar Class X Board Triangles Questions
- In any \(\triangle ABC\), \(\angle A = 90^\circ\), BC = 13 cm, AB = 12 cm; then the value of AC is
- In \(\triangle DEF\) and \(\triangle PQR\) it is given that \(\angle D = \angle Q\) and \(\angle R = \angle E\), then which of the following is correct?
- ABC is an isosceles right triangle with C as right angle. Prove that \(AB^2 = 2AC^2\).
- In \(\triangle ABC\), points \(X\) on \(AB\) and \(Y\) on \(AC\) satisfy \(XY\parallel BC\). If \(AX:XB=2:3\), then \(AY:YC=\) ?
- The ratio of the areas of two similar triangles is \(121:64\). The ratio of their corresponding medians is:
View More Questions
Top Bihar Class X Board Questions
- Jim says that women use too many ........................ things.
- R. C. Hutchinson in 'The Pace for Living' describes the ........................ of modern man.
- According to Jim, nobody's willing to do anything about ........................ .
- The squirrel was considered an easy prey by the ........................ .
- The author enjoys travelling fast in a ........................ if it is not his own.
View More Questions