jeanine08181977
Answered

The formula for the surface area, [tex]A[/tex], of a prism is given by

[tex]\[A = 2lw + 2lh + 2wh,\][/tex]

where [tex]l[/tex] is the length of the prism, [tex]w[/tex] is the width, and [tex]h[/tex] is the height.

Which formula is the result of solving the formula for [tex]l[/tex]?

[tex]\[
A. \quad l = \frac{2A - wh}{w + h}
\][/tex]
[tex]\[
B. \quad l = \frac{A - 2h(l + w)}{2w}
\][/tex]
[tex]\[
C. \quad l = \frac{A - 2wh}{2(w + h)}
\][/tex]
[tex]\[
D. \quad l = \frac{2wh - A}{2(w + h)}
\][/tex]



Answer :

GinnyAnswer
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)}
\