To solve the problem of finding the length and height of a rectangular prism given its width and volume, we need to follow a step-by-step approach.
1. Understand the given information:
- Width of the rectangular prism: 3 inches.
- The length is twice the height.
- Volume of the rectangular prism: 24 cubic inches.
2. Define the variables:
- Let [tex]\( h \)[/tex] represent the height of the rectangular prism.
- Since the length is twice the height, we can represent the length as [tex]\( 2h \)[/tex].
3. Write the formula for the volume of a rectangular prism:
[tex]\[
\text{Volume} = \text{length} \times \text{width} \times \text{height}
\][/tex]
4. Substitute the known values into the formula:
[tex]\[
24 = 2h \times 3 \times h
\][/tex]
Simplify the expression on the right-hand side:
[tex]\[
24 = 6h^2
\][/tex]
5. Solve for [tex]\( h \)[/tex]:
Divide both sides of the equation by 6 to isolate [tex]\( h^2 \)[/tex]:
[tex]\[
h^2 = \frac{24}{6}
\][/tex]
[tex]\[
h^2 = 4
\][/tex]
Take the square root of both sides to solve for [tex]\( h \)[/tex]:
[tex]\[
h = \sqrt{4}
\][/tex]
[tex]\[
h = 2
\][/tex]
6. Find the length:
Since the length is twice the height:
[tex]\[
\text{length} = 2h = 2 \times 2 = 4
\][/tex]
7. Summarize the results:
- Height ([tex]\( h \)[/tex]) of the portable charger is 2 inches.
- Length of the portable charger is 4 inches.
Therefore, the height of the portable charger is 2 inches, and its length is 4 inches.
