Sure! Let's start from the given formula for the volume of a rectangular prism:
[tex]\[ V = l \cdot w \cdot h \][/tex]
where:
- [tex]\( V \)[/tex] is the volume,
- [tex]\( l \)[/tex] is the length of the base,
- [tex]\( w \)[/tex] is the width of the base,
- [tex]\( h \)[/tex] is the height of the prism.
Our goal is to find the width [tex]\( w \)[/tex] when the volume [tex]\( V \)[/tex], the length [tex]\( l \)[/tex], and the height [tex]\( h \)[/tex] are already known.
To isolate [tex]\( w \)[/tex], we need to rearrange the formula. We do this by dividing both sides of the equation by [tex]\( l \cdot h \)[/tex]:
[tex]\[ \frac{V}{l \cdot h} = \frac{l \cdot w \cdot h}{l \cdot h} \][/tex]
This simplifies to:
[tex]\[ w = \frac{V}{l \cdot h} \][/tex]
Therefore, to find the width [tex]\( w \)[/tex], we can use the formula:
[tex]\[ w = \frac{V}{l \cdot h} \][/tex]
Let's plug in the given values as an example. Suppose the volume [tex]\( V \)[/tex] of the prism is 100 cubic units, the length [tex]\( l \)[/tex] of the base is 5 units, and the height [tex]\( h \)[/tex] of the prism is 4 units. Then:
[tex]\[ w = \frac{100}{5 \cdot 4} \][/tex]
Calculate the denominator first:
[tex]\[ 5 \cdot 4 = 20 \][/tex]
Then divide the volume by this product:
[tex]\[ w = \frac{100}{20} = 5 \][/tex]
So, the width [tex]\( w \)[/tex] of the base of the prism is 5 units.
The correct answer is:
[tex]\[ w = \frac{V}{l \cdot h} \][/tex]
