The dimensions of a rectangular prism are all whole numbers greater than 1". If the volume is 165 cu", and the height is 5", what is the perimeter of the base?
V = LWH
165 = 5 * L * W
165/5 = L * W
33 = L * W
To find the perimeter of the base of a rectangular prism, we need to determine the dimensions of the base. Since the height is given as 5 inches, it means that one of the sides of the base is 5 inches.
To find the other side of the base, we can divide the volume of the prism by the product of the given height and the known dimension of the base. In this case, the volume is 165 cu", the height is 5", and one side of the base is 5". So, we have:
165 cu" = (side of base) * 5" * 5"
Now, let's solve for the side of the base:
(side of base) = 165 cu" / (5" * 5")
(side of base) = 165 cu" / 25
Calculating the result:
(side of base) = 6.6"
Since the dimensions are stated to be whole numbers greater than 1 inch, we can conclude that the side of the base is 6 inches.
Now, a rectangular prism has two identical sides and two pairs of identical sides. Therefore, the perimeter of the base is:
Perimeter of base = 2 * (length + width)
= 2 * (6" + 5")
= 2 * 11"
= 22"
Hence, the perimeter of the base is 22 inches.