The volume of a right rectangular prism is
volume = length * width * height
Let's abbreviate it to
V = LWH
The length and width are the side of the base. We are told the base is a square, so the length and width are equal. The perimeter of the base is 4 times the length, and that equals the height.
L = L (unknown)
W = L (we express the width in terms of the length)
P = 4L (the perimeter of the base in terms of the length)
P = H (the perimeter of the base equals the height)
H = 4L (height in terms of the length)
Since everything is expressed in terms of the length, we have only one variable, L. Now we can solve for L.
V = LWH
108 = L * L * 4L
4L^3 = 108
L^3 = 27
L = 3
The length is 3 in., so the width is also 3 in. The height is 4 * 3 in. = 12 in.
Answer:
Length = 3 in.
Width = 3 in.
Height = 12 in.
