Sure, let's solve the area formula [tex]\( A = l \cdot w \)[/tex] for [tex]\( l \)[/tex].
Step-by-Step Solution:
1. Start with the given formula:
[tex]\[
A = l \cdot w
\][/tex]
2. Rearrange the formula to solve for [tex]\( l \)[/tex].
To isolate [tex]\( l \)[/tex], you need to divide both sides of the equation by [tex]\( w \)[/tex]:
[tex]\[
l = \frac{A}{w}
\][/tex]
So, the length [tex]\( l \)[/tex] in terms of area [tex]\( A \)[/tex] and width [tex]\( w \)[/tex] is given by:
[tex]\[
I = l = \frac{A}{w}
\][/tex]
This matches the correct choice from your provided list:
[tex]\[
I = \frac{A}{w}
\][/tex]
Thus, the correct answer is:
[tex]\[
I = \frac{A}{w}
\][/tex]
This completes the solution to rearranging the area formula [tex]\( A = l \cdot w \)[/tex] for [tex]\( l \)[/tex].
