Question

Consider the formula S = 12lp + Bwhich is used to find the surface area of a square-based pyramid. Which of the following correctly rearranges the formula for the quantity of interest p?(1 point)Responsesp = 2(S − B)lp equals Start Fraction 2 left parenthesis upper S minus upper B right parenthesis over l End Fractionp = l2S − 2Bp equals Start Fraction l over upper 2 S minus 2 upper B End Fractionp = S − B −l2p equals upper S minus upper B minus Start Fraction l over 2 End Fractionp = 2S − Bl

Answer 1

To rearrange the formula \( S = 12lp + B \) for \( p \), we need to isolate \( p \) on one side of the equation.

1. Start with the original formula:
\[
S = 12lp + B
\]

2. Subtract \( B \) from both sides:
\[
S - B = 12lp
\]

3. Now, divide both sides by \( 12l \) to solve for \( p \):
\[
p = \frac{S - B}{12l}
\]

None of the options listed match \( p = \frac{S - B}{12l} \) directly, but it looks like there may be a mistake in how the question was presented with regards to the coefficient in front of \( lp \).

If you meant \( S = lp + B \), then:

1. Start with the original formula:
\[
S = lp + B
\]

2. Subtract \( B \):
\[
S - B = lp
\]

3. Divide by \( l \):
\[
p = \frac{S - B}{l}
\]

If you're looking for the rearranged form in the options provided, please clarify. Otherwise, the correct form derived is \( p = \frac{S - B}{12l} \) or \( p = \frac{S - B}{l} \) based on the original formula used.