Certainly! Let's solve for [tex]\( P \)[/tex] given the formula for the surface area of a rectangular pyramid [tex]\( S = lw + 0.5Ph \)[/tex] and the given values.
Given:
- [tex]\( S = 8 \)[/tex] (surface area)
- [tex]\( l = 5 \)[/tex] (length)
- [tex]\( w = 5 \)[/tex] (width)
- [tex]\( h = 0.5 \)[/tex] (height)
We need to solve for [tex]\( P \)[/tex], and the formula given is:
[tex]\[ P = \frac{S - lw}{0.5h} \][/tex]
Let’s break this down step by step:
1. Calculate [tex]\( lw \)[/tex]:
[tex]\[ lw = 5 \times 5 = 25 \][/tex]
2. Subtract [tex]\( lw \)[/tex] from [tex]\( S \)[/tex]:
[tex]\[ S - lw = 8 - 25 = -17 \][/tex]
3. Calculate the denominator [tex]\( 0.5h \)[/tex]:
[tex]\[ 0.5h = 0.5 \times 0.5 = 0.25 \][/tex]
4. Divide the result of Step 2 by the result of Step 3:
[tex]\[ P = \frac{-17}{0.25} = -68 \][/tex]
Therefore, the value of [tex]\( P \)[/tex] is:
[tex]\[ P = -68 \][/tex]
So, the detailed step-by-step solution for [tex]\( P \)[/tex] given the values is [tex]\( P = -68 \)[/tex].
