Question

If the volume of a right rectangular prism is
1.5 in
.
3
1.5 in.3 and its length and width have a product of
1.5 in
.
2
1.5 in.2, what is the height of this prism?(1 point)

Answer 1

To find the height of the right rectangular prism, we can use the formula for the volume of a rectangular prism, which is:

\[
\text{Volume} = \text{Length} \times \text{Width} \times \text{Height}
\]

Given that the volume of the prism is \(1.5 \, \text{in}^3\) and the product of the length and width is \(1.5 \, \text{in}^2\), we can denote:

- Length \(\times\) Width = \(1.5 \, \text{in}^2\)
- Volume = \(1.5 \, \text{in}^3\)

Let \(L\) be the length and \(W\) be the width. Thus, we have:

\[
L \times W = 1.5 \, \text{in}^2
\]
\[
V = L \times W \times H = 1.5 \, \text{in}^3
\]

We can rearrange the volume formula to solve for height \(H\):

\[
H = \frac{V}{L \times W}
\]

Substituting the given values:

\[
H = \frac{1.5 \, \text{in}^3}{1.5 \, \text{in}^2}
\]

Calculating this gives:

\[
H = 1.0 \, \text{in}
\]

Thus, the height of the prism is:

\[
\boxed{1.0 \, \text{in}}
\]