Answer

Verified

380.7k+ views

**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.

Recently Updated Pages

How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE

Why Are Noble Gases NonReactive class 11 chemistry CBSE

Let X and Y be the sets of all positive divisors of class 11 maths CBSE

Let x and y be 2 real numbers which satisfy the equations class 11 maths CBSE

Let x 4log 2sqrt 9k 1 + 7 and y dfrac132log 2sqrt5 class 11 maths CBSE

Let x22ax+b20 and x22bx+a20 be two equations Then the class 11 maths CBSE

Trending doubts

Which are the Top 10 Largest Countries of the World?

The 3 + 3 times 3 3 + 3 What is the right answer and class 8 maths CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

How many crores make 10 million class 7 maths CBSE

Difference Between Plant Cell and Animal Cell

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Change the following sentences into negative and interrogative class 10 english CBSE

Write a letter to the principal requesting him to grant class 10 english CBSE