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Bonnie has a container in the shape of a rectangular pyramid. The formula for the surface area of the enclosed space is [tex]S = lw + 0.5Ph[/tex]. Solve for [tex]P[/tex].

A. [tex]P = 8 \quad \mu \quad 0.5h[/tex]
B. [tex]P = 5 + -w + 0.5h[/tex]
C. [tex]P = \frac{S - lw}{0.5h}[/tex]
D. [tex]P = \frac{S}{w + 0.5h}[/tex]

Sagot :

GinnyAnswer
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].
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