Question

A rectangular prism has a length of
(
2
x
+
5
)
, a width of
(
2
x
−
5
)
, and a height of
(
3
x
)
. Mr. Jinks calculated the volume and got
12
x
3
−
75
x
square inches. Is his answer true or false?

A.
True


B.
False

Answer 1

To find the volume \( V \) of a rectangular prism, we use the formula:

\[
V = \text{length} \times \text{width} \times \text{height}
\]

Given:
- Length \( l = 2x + 5 \)
- Width \( w = 2x - 5 \)
- Height \( h = 3x \)

We can calculate the volume as follows:

\[
V = (2x + 5)(2x - 5)(3x)
\]

First, we will calculate \( (2x + 5)(2x - 5) \) using the difference of squares:

\[
(2x + 5)(2x - 5) = (2x)^2 - (5)^2 = 4x^2 - 25
\]

Now, we multiply this result by the height \( 3x \):

\[
V = (4x^2 - 25)(3x)
\]

Distributing \( 3x \):

\[
V = 3x(4x^2) - 3x(25)
\]
\[
V = 12x^3 - 75x
\]

Now we compare this with Mr. Jinks's result, which is \( 12x^3 - 75x \).

Since our calculation matches Mr. Jinks's result, his answer is indeed correct.

The answer is:

**A. True**