Sure, let's solve this step by step!
Given:
- The area of one side of the rectangular prism is [tex]\( 72 \, \text{cm}^2 \)[/tex].
- The volume of the rectangular prism is [tex]\( 360 \, \text{cm}^3 \)[/tex].
Let's denote the dimensions of the rectangular prism as [tex]\( a \)[/tex], [tex]\( b \)[/tex], and [tex]\( c \)[/tex].
1. The area of one side can be expressed as:
[tex]\[
a \times b = 72 \, \text{cm}^2
\][/tex]
This equation tells us that the product of the two dimensions (length and width) of the rectangle forming one side of the prism is 72.
2. The volume of the rectangular prism can be expressed as:
[tex]\[
a \times b \times c = 360 \, \text{cm}^3
\][/tex]
This equation tells us that the product of the dimensions (length, width, and height) of the prism is 360.
3. We already know from the first equation that [tex]\( a \times b = 72 \)[/tex].
Therefore, we can substitute [tex]\( a \times b \)[/tex] into the volume equation:
[tex]\[
72 \times c = 360
\][/tex]
4. Now, solve for the unknown edge [tex]\( c \)[/tex]:
[tex]\[
c = \frac{360}{72}
\][/tex]
5. Perform the division:
[tex]\[
c = 5
\][/tex]
Therefore, the length of the unknown edge of the rectangular prism is [tex]\( 5 \, \text{cm} \)[/tex].
