Chapter 7.6, Problem 9ST2

To determine

To find: The value of x.

Answer to Problem 9ST2

  $x=12$

Explanation of Solution

Given information:

Calculation:

Let the triangle be $ABC$ and $DE$ be the parallel line.

According to Triangle Proportionality Theorem, if a line parallel to one side of a triangle intersects the other two sides, then it divides those sides proportionally.

Then, from the figure,

  $\begin{array}{l}\frac{BD}{DA}=\frac{BE}{EC}\\ \Rightarrow \frac{BA-DA}{DA}=\frac{BE}{BC-BE}\\ \Rightarrow \frac{15-6}{6}=\frac{x}{20-x}\\ \Rightarrow \frac{9}{6}=\frac{x}{20-x}\end{array}$

  $\begin{array}{l}\Rightarrow 9\times (20-x)=x\times 6\\ \Rightarrow 180-9x=6x\\ \Rightarrow 6x+9x=180\\ \Rightarrow 15x=180\\ \Rightarrow x=\frac{180}{15}\\ \Rightarrow x=12\end{array}$

Thus, the value of x is 12.