Question

If $13=\frac{13w}{1-w}$, Then ${\left(2w\right)}^2=?$

• A. $\frac{1}{4}$
• B. $\frac{1}{2}$
• C. $1$
• D. $2$

Answer 1

The correct option is C

$1$

Explanation for the correct option:

Step $1:$ Compute the value of $w$.

Solve the given equation for $w$.

$13=\frac{13w}{1-w}$

Divide both sides by $13$.

$1=\frac{w}{1-w}$

Multiply both sides by $1-w$.

$1-w=w$

Add $w$ on both sides.

$1=2w$

Divide both sides by $w$.

$w=\frac{1}{2}$

Step $2:$ Calculate the required value.

Since the value of $w$ is $\frac{1}{2}$.

$$\begin{gathered} {\left(2w\right)}^2={\left(2\times \frac{1}{2}\right)}^2 \\ \Rightarrow {\left(2w\right)}^2={\left(1\right)}^2 \\ \Rightarrow {\left(2w\right)}^2=1 \end{gathered}$$

Since the value of ${\left(2w\right)}^2$ is $1$.

Hence, option $C$ is the correct answer.