Question

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

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:

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

In this problem, we are given:

- Volume = 1.5 in³
- Length × Width = 1.5 in²

Let's denote:

- Length = L
- Width = W
- Height = H

We know that:

\[
L \times W = 1.5 \text{ in}^2
\]

And we know the volume is given by:

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

Substituting \(L \times W\) into the volume formula gives:

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

Now, to find the height \(H\), we can divide both sides of the equation by \(1.5 \text{ in}^2\):

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

This simplifies to:

\[
H = 1 \text{ in}
\]

Thus, the height of the prism is:

\[
\boxed{1 \text{ in}}
\]