To find the height of a rectangular prism when given the area of a cross-section perpendicular to the base and the dimensions of the base, follow these steps:
1. Understand the given data:
- The area of the cross-section perpendicular to the base is 45 square inches.
- The length of the base is 5 inches.
- The width of the base is 5 inches.
2. Recall that the cross-section perpendicular to the base is a side face of the prism.
The area of this face can be represented as the product of one of the base dimensions (length or width) and the height of the prism.
3. Set up the equation:
- Since the area of the cross-section is 45 square inches, and one of the base dimensions (say length) is 5 inches, the relationship can be expressed as:
[tex]\[
\text{Area of cross-section} = \text{length of base} \times \text{height of prism}
\][/tex]
[tex]\[
45 \text{ square inches} = 5 \text{ inches} \times \text{height of prism}
\][/tex]
4. Solve for the height of the prism:
- Divide both sides of the equation by the length of the base (5 inches):
[tex]\[
\text{height of prism} = \frac{45 \text{ square inches}}{5 \text{ inches}}
\][/tex]
Simplifying the right-hand side:
[tex]\[
\text{height of prism} = 9 \text{ inches}
\][/tex]
Thus, the height of the prism is [tex]\( 9 \)[/tex] inches.
