Question

In $\Delta$ ABC, DE || BC. If AD = x - 5, DB = 3x - 19, AE = 3 and EC = x - 3. Then which of the following could be the value of x?

• A. 9
• B. 5
• C. 8
• D. 4

Answer 1

Answer: (A), (C)

The correct options are
A

9

C

8

In the triangle ABC, DE || BC (Given)

Using Basic Proportionality Theorem, we have
$\begin{array}{cc}& \frac{AD}{DB}=\frac{AE}{EC}\\ \Rightarrow & \frac{x-5}{3x-19}=\frac{3}{x-3}\\ \Rightarrow & (x-5)(x-3)=3(3x-19)\\ \Rightarrow & x^2-3x-5x+15=9x-57\\ \Rightarrow & x^2-17x+72=0\\ \Rightarrow & x^2-9x-8x+72=0\\ \Rightarrow & x(x-9)-8(x-9)=0\\ \Rightarrow & (x-9)(x-8)=0\\ \Rightarrow & x-9=0orx-8=0\\ \Rightarrow & x=9orx=8\end{array}$