Solve for l s=n/2*(a+l)

$s = \frac{n}{2} \cdot (a + l)$

Step 1

Rewrite the equation as $\frac{n}{2} \cdot (a + l) = s$ .

$\frac{n}{2} \cdot (a + l) = s$

Step 2

Multiply each term in $\frac{n}{2} \cdot (a + l) = s$ by $\frac{2}{n}$ to eliminate the fractions.

Multiply each term in $\frac{n}{2} \cdot (a + l) = s$ by $\frac{2}{n}$ .

$\frac{n}{2} \cdot (a + l) \frac{2}{n} = s \frac{2}{n}$

Simplify the left side.

Simplify terms.

Apply the distributive property.

$(\frac{n}{2} a + \frac{n}{2} l) \frac{2}{n} = s \frac{2}{n}$

Combine $\frac{n}{2}$ and $a$ .

$(\frac{n a}{2} + \frac{n}{2} l) \frac{2}{n} = s \frac{2}{n}$

Combine $\frac{n}{2}$ and $l$ .

$(\frac{n a}{2} + \frac{n l}{2}) \frac{2}{n} = s \frac{2}{n}$

Multiply $\frac{n a}{2} + \frac{n l}{2}$ by $\frac{2}{n}$ .

$\frac{(\frac{n a}{2} + \frac{n l}{2}) \cdot 2}{n} = s \frac{2}{n}$

Simplify the numerator.

Combine the numerators over the common denominator.

$\frac{\frac{n a + n l}{2} \cdot 2}{n} = s \frac{2}{n}$

Factor $n$ out of $n a + n l$ .

Factor $n$ out of $n a$ .

$\frac{\frac{n (a) + n l}{2} \cdot 2}{n} = s \frac{2}{n}$

Factor $n$ out of $n l$ .

$\frac{\frac{n (a) + n (l)}{2} \cdot 2}{n} = s \frac{2}{n}$

Factor $n$ out of $n (a) + n (l)$ .

$\frac{\frac{n (a + l)}{2} \cdot 2}{n} = s \frac{2}{n}$

Combine $\frac{n (a + l)}{2}$ and $2$ .

$\frac{\frac{n (a + l) \cdot 2}{2}}{n} = s \frac{2}{n}$

Reduce the expression by cancelling the common factors.

Reduce the expression $\frac{n (a + l) \cdot 2}{2}$ by cancelling the common factors.

Cancel the common factor.

$\frac{\frac{n (a + l) \cdot 2}{2}}{n} = s \frac{2}{n}$

Rewrite the expression.

$\frac{\frac{n (a + l)}{1}}{n} = s \frac{2}{n}$

Divide $n (a + l)$ by $1$ .

$\frac{n (a + l)}{n} = s \frac{2}{n}$

Cancel the common factor of $n$ .

Cancel the common factor.

$\frac{n (a + l)}{n} = s \frac{2}{n}$

Divide $a + l$ by $1$ .

$a + l = s \frac{2}{n}$

Simplify the right side.

Combine $s$ and $\frac{2}{n}$ .

$a + l = \frac{s \cdot 2}{n}$

Move $2$ to the left of $s$ .

$a + l = \frac{2 s}{n}$

Step 3

Subtract $a$ from both sides of the equation.

$l = \frac{2 s}{n} - a$

Solve for l s=n/2*(a+l)

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