Question

The surface area S of a right pyramid is given by S=12P+B

, where P is the perimeter of the base,
is the slant height, and B is the area of the base. Solve for .




=



,

Answer 1

Step-by-step explanation:To solve for the slant height \(l\) in terms of the given variables, we need to rearrange the formula \(S = 12P + B\) by isolating \(l\) on one side of the equation. Here's how to do it step by step:

Given formula: \(S = 12P + B\)

Substitute the value of \(S\) using the formula for the surface area of a pyramid: \(S = \frac{1}{2}Pl + B\)

Equating the two expressions for \(S\): \(\frac{1}{2}Pl + B = 12P + B\)

Subtract \(B\) from both sides: \(\frac{1}{2}Pl = 12P\)

Divide both sides by \(\frac{1}{2}P\): \(l = 24\)

Therefore, the expression for the slant height \(l\) is \(24\).