Chapter 5.7, Problem 39HP

(a)

To determine

To solve: The proportion $\frac{4}{x}=\frac{x}{9}$ .

Answer to Problem 39HP

The solution of the proportion $\frac{4}{x}=\frac{x}{9}$ are $x=\pm 6$ .

Explanation of Solution

Given information:

The proportion is $\frac{4}{x}=\frac{x}{9}$ .

Calculation:

Simplify the given proportion.

  $\begin{array}{c}\frac{4}{x}=\frac{x}{9}\\ x\times x=9\times 4\\ x^2=36\end{array}$

Further simplify,

  $\begin{array}{c}{x}^2=36\\ x=\pm \sqrt{36}\\ x=\pm 6\end{array}$

Therefore, the solution of the proportion $\frac{4}{x}=\frac{x}{9}$ are $x=\pm 6$ .

(b)

To determine

To solve: The proportion $\frac{2}{x}=\frac{x}{8}$ .

Answer to Problem 39HP

The solution of the proportion $\frac{2}{x}=\frac{x}{8}$ are $x=\pm 4$ .

Explanation of Solution

Given information:

The proportion is $\frac{2}{x}=\frac{x}{8}$ .

Calculation:

Simplify the given proportion.

  $\begin{array}{c}\frac{2}{x}=\frac{x}{8}\\ x\times x=8\times 2\\ x^2=16\end{array}$

Further simplify,

  $\begin{array}{c}{x}^2=16\\ x=\pm \sqrt{16}\\ x=\pm 4\end{array}$

Therefore, the solution of the proportion $\frac{2}{x}=\frac{x}{8}$ are $x=\pm 4$ .

(c)

To determine

To solve: The proportion $\frac{4}{x}=\frac{x}{25}$ .

Answer to Problem 39HP

The solution of the proportion $\frac{4}{x}=\frac{x}{25}$ are $x=\pm 10$ .

Explanation of Solution

Given information:

The proportion is $\frac{4}{x}=\frac{x}{25}$ .

Calculation:

Simplify the given proportion.

  $\begin{array}{c}\frac{4}{x}=\frac{x}{25}\\ x\times x=25\times 4\\ x^2=100\end{array}$

Further simplify,

  $\begin{array}{c}{x}^2=100\\ x=\pm \sqrt{100}\\ x=\pm 10\end{array}$

Therefore, the solution of the proportion $\frac{4}{x}=\frac{x}{25}$ are $x=\pm 10$ .

(d)

To determine

To solve: The proportion $\frac{9}{x}=\frac{x}{16}$ .

Answer to Problem 39HP

The solution of the proportion $\frac{9}{x}=\frac{x}{16}$ are $x=\pm 12$ .

Explanation of Solution

Given information:

The proportion is $\frac{9}{x}=\frac{x}{16}$ .

Calculation:

Simplify the given proportion.

  $\begin{array}{c}\frac{9}{x}=\frac{x}{16}\\ x\times x=9\times 16\\ x^2=144\end{array}$

Further simplify,

  $\begin{array}{c}{x}^2=144\\ x=\pm \sqrt{144}\\ x=\pm 12\end{array}$

Therefore, the solution of the proportion $\frac{9}{x}=\frac{x}{16}$ are $x=\pm 12$ .