To find the width [tex]\( w \)[/tex] of the base of a rectangular prism when the volume [tex]\( V \)[/tex], length of the base [tex]\( l \)[/tex], and height of the prism [tex]\( h \)[/tex] are known, follow these steps:
1. Start with the given formula for the volume of a rectangular prism:
[tex]\[
V = l \cdot w \cdot h
\][/tex]
2. To isolate [tex]\( w \)[/tex], divide both sides of the equation by [tex]\( l \cdot h \)[/tex]:
[tex]\[
\frac{V}{l \cdot h} = w
\][/tex]
So, the formula to find the width [tex]\( w \)[/tex] of the base of the prism is:
[tex]\[
w = \frac{V}{l \cdot h}
\][/tex]
Plugging in the known values [tex]\( V = 27 \)[/tex], [tex]\( l = 3 \)[/tex], and [tex]\( h = 3 \)[/tex], we get:
[tex]\[
w = \frac{27}{3 \cdot 3}
\][/tex]
Thus, the width [tex]\( w \)[/tex] of the base of the prism is:
[tex]\[
w = 3.0
\][/tex]
