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The area of a cross section perpendicular to the base of a rectangular prism is 45 square inches. If the length and width of the base are 5 inches each,
what is the height of the prism?
The height of the prism is
inches.
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Answer :

To find the height of the rectangular prism, we start by understanding that the area of the cross section perpendicular to the base is given as 45 square inches. The cross-section area in a rectangular prism is calculated by multiplying the base area by the height of the prism.

First, let's calculate the base area of the prism. The base of the prism is a rectangle with:
- Length = 5 inches
- Width = 5 inches

The area of the base (A_base) is given by:
[tex]\[ A_\text{base} = \text{length} \times \text{width} \][/tex]
[tex]\[ A_\text{base} = 5 \, \text{inches} \times 5 \, \text{inches} = 25 \, \text{square inches} \][/tex]

Next, we know the cross-section area (A_cross-section) is 45 square inches. The cross-section area is also the product of the base area and the height of the prism (h):

[tex]\[ A_\text{cross-section} = A_\text{base} \times h \][/tex]

Substituting the given values:

[tex]\[ 45 \, \text{square inches} = 25 \, \text{square inches} \times h \][/tex]

To find the height [tex]\( h \)[/tex], we solve for [tex]\( h \)[/tex] by dividing both sides of the equation by the base area:

[tex]\[ h = \frac{45 \, \text{square inches}}{25 \, \text{square inches}} \][/tex]

[tex]\[ h = 1.8 \][/tex]

Therefore, the height of the prism is [tex]\( 1.8 \)[/tex] inches.