A rectangular prism has a base area of 25 in.2 and a volume of 125 in.3 . If a rectangular pyramid has a congruent base and height congruent to the prism, what is the height of the pyramid?
First, let's find the dimensions of the rectangular prism.
Let's assume the length of the base of the rectangular prism is l, the width is w, and the height is h.
Given that the base area of the prism is 25 in^2 and the volume is 125 in^3, we have:
lw = 25 (1)
lwh = 125 (2)
From equation (1), we can express w in terms of l: w = 25/l
Substitute w = 25/l into equation (2):
l * 25/l * h = 125
25h = 125
h = 125/25
h = 5
So, the dimensions of the rectangular prism are l = 5, w = 5, and h = 5.
Since the rectangular pyramid has a congruent base and height to the prism, the height of the pyramid is also 5 inches.