To solve the formula for the surface area of a prism, given by [tex]\( A = 2lw + 2lh + 2wh \)[/tex], for [tex]\( l \)[/tex], follow these detailed steps:
1. Start with the given formula:
[tex]\[
A = 2lw + 2lh + 2wh
\][/tex]
2. Isolate the terms involving [tex]\( l \)[/tex] on one side of the equation. This can be achieved by subtracting [tex]\( 2wh \)[/tex] from both sides:
[tex]\[
A - 2wh = 2lw + 2lh
\][/tex]
3. Factor out [tex]\( l \)[/tex] from the terms on the right-hand side:
[tex]\[
A - 2wh = 2l(w + h)
\][/tex]
4. Solve for [tex]\( l \)[/tex] by dividing both sides of the equation by [tex]\( 2(w + h) \)[/tex]:
[tex]\[
l = \frac{A - 2wh}{2(w + h)}
\][/tex]
Thus, the formula for [tex]\( l \)[/tex] is:
[tex]\[
l = \frac{A - 2wh}{2(w + h)}
\][/tex]
Among the given options, the correct formula is:
\[
l = \frac{A - 2wh}{2(w + h)}
\
