Sure! Let's solve for [tex]\( l \)[/tex] in the formula [tex]\( s = \frac{n}{2} (a + l) \)[/tex] step-by-step.
1. Start with the formula:
[tex]\[
s = \frac{n}{2} (a + l)
\][/tex]
2. Multiply both sides by [tex]\( 2 \)[/tex] to eliminate the fraction:
[tex]\[
2s = n (a + l)
\][/tex]
3. Divide both sides by [tex]\( n \)[/tex] to isolate [tex]\( a + l \)[/tex]:
[tex]\[
\frac{2s}{n} = a + l
\][/tex]
4. Subtract [tex]\( a \)[/tex] from both sides to solve for [tex]\( l \)[/tex]:
[tex]\[
l = \frac{2s}{n} - a
\][/tex]
Now, let's substitute the given values [tex]\( s = 55 \)[/tex], [tex]\( n = 10 \)[/tex], and [tex]\( a = 1 \)[/tex]:
5. Substitute [tex]\( s = 55 \)[/tex], [tex]\( n = 10 \)[/tex], and [tex]\( a = 1 \)[/tex] into the equation:
[tex]\[
l = \frac{2 \times 55}{10} - 1
\][/tex]
6. Calculate the multiplication and division:
[tex]\[
l = \frac{110}{10} - 1
\][/tex]
7. Simplify the division:
[tex]\[
l = 11 - 1
\][/tex]
8. Finally, subtract 1:
[tex]\[
l = 10
\][/tex]
Hence, the value of [tex]\( l \)[/tex] is [tex]\( \boxed{10} \)[/tex].
