To solve for [tex]\( P \)[/tex] from the given surface area formula [tex]\( S = h \cdot w + 0.5 \cdot P \cdot h \)[/tex], follow these steps:
1. Write the given equation:
[tex]\[
S = h \cdot w + 0.5 \cdot P \cdot h
\][/tex]
2. Isolate the term involving [tex]\( P \)[/tex]:
Subtract [tex]\( h \cdot w \)[/tex] from both sides of the equation:
[tex]\[
S - h \cdot w = 0.5 \cdot P \cdot h
\][/tex]
3. Eliminate the coefficient 0.5:
Multiply both sides of the equation by 2 to eliminate the 0.5 coefficient:
[tex]\[
2 \cdot (S - h \cdot w) = P \cdot h
\][/tex]
4. Solve for [tex]\( P \)[/tex]:
Divide both sides of the equation by [tex]\( h \)[/tex]:
[tex]\[
P = \frac{2 \cdot (S - h \cdot w)}{h}
\][/tex]
5. Compare the derived formula with the given options:
- Option 1: [tex]\( P = S - I w = 0.5 h \)[/tex]
- Option 2: [tex]\( P = S + W + 0.5 h \)[/tex]
- Option 3: [tex]\( P = \frac{S - W}{0.5 h} \)[/tex]
- Option 4: [tex]\( P = \frac{S}{\sqrt{W + 0.5 h}} \)[/tex]
None of these provided options match our derived formula:
[tex]\[ P = \frac{2 \cdot (S - h \cdot w)}{h} \][/tex]
Conclusion:
None of the given choices are correct.
