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**Hint:**This question is related to linear equation concept. An equation for a straight line is known as a linear equation. The term which is involved in a linear equation is either a constant or a single variable or product of a constant. The two variables can never be multiplied. All linear equations have a line graph. Linear equations are the same as linear function. The general form of writing a linear equation is$y = mx + c$ and $m$ is not equal to zero, where $m$ is the slope and $c$ is the point on which it cuts the y-axis. $y = mx + c$ is also known as the equation of the line in slope-intercept form. This given question deals with a specific type of linear equation and that is, formulas for problem solving.

**Complete step by step solution:**

Given is $A = \dfrac{r}{{2L}}$

We have to solve the given equation in order to find the value of $L$ for which the left-hand side is equal to the right-hand side of the equation.

Let us simply start by simplifying the given equation by multiplying both sides of the equation by $2$.

$

\Rightarrow A = \dfrac{r}{{2L}} \\

\Rightarrow A \times 2 = \dfrac{r}{{2L}} \times 2 \\

\Rightarrow 2A = \dfrac{r}{L} \\

$

Next, let us multiply $L$ on both the sides of the equation and we get,

$

\Rightarrow 2A = \dfrac{r}{L} \\

\Rightarrow 2A \times L = \dfrac{r}{L} \times L \\

\Rightarrow 2AL = r \\

$

Now, we isolate $L$ on the left-hand side of the equation by dividing both the sides of the equation by $2A$ and we get,

$

\Rightarrow 2AL = r \\

\Rightarrow \dfrac{{2AL}}{{2A}} = \dfrac{r}{{2A}} \\

\Rightarrow L = \dfrac{r}{{2A}} \\

$

**Therefore, the value of $L$ is $\dfrac{r}{{2A}}$.**

**Note:**Now that we know the value of $L$ is $\dfrac{r}{{2A}}$, there is a way to double check our answer. In order to double check the solution we are supposed to substitute the value of $L$ which we got as

$\dfrac{r}{{2A}}$ in the given equation, $A = \dfrac{r}{{2L}}$

$

\Rightarrow A = \dfrac{r}{{2L}} \\

\Rightarrow A = \dfrac{r}{{2\left( {\dfrac{r}{{2A}}} \right)}} \\

\Rightarrow A = \dfrac{r}{2} \times \dfrac{{2A}}{r} \\

\Rightarrow A = A \\

$

Now, the left-hand side is equal to the right-hand side of the equation. So, we can conclude that our solution or the value of $L$ which we calculated was correct.

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