Chapter 11, Problem 1STP

To determine

To Find: The value of the $x$ in the given figure.

Answer to Problem 1STP

The correct option is B.

Explanation of Solution

Given:

The given diagram is shown in Figure 1

  

Figure 1

Calculation:

Consider the geometric mean altitude theorem as,

  $\begin{array}{l}{14}^2=2x\left(3x-7\right)\\ 196=6x^2-14x\\ 3x^2-7x-98=0\end{array}$

Then, the zero of the polynomial is,

  $\begin{array}{c}x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}\\ =\frac{-\left(-7\right)\pm \sqrt{\left(-7\right)-4\left(3\right)\left(-98\right)}}{2\left(3\right)}\\ =\frac{7\pm 35}{6}\\ =\frac{-14}{3},7\end{array}$

Consider the solution is,

  $x=7$

Thus, the correct option is B