Jack has 222 lego cubes, each of side length 1. He puts them together to form a rectangular prism. If the perimeter of the base of the prism is 10, what is the height of the prism?
Your numbers require dimensions. Inches? Centimeters? Meters?
22.2
meter
Perimeter=10, therefore sum of two sides =5.
Try sides 2 and 3, area=6, so height=222/6=37.
Height=37.
thanks
To find the height of the rectangular prism, we need to determine the number of lego cubes used for each dimension of the base.
Let's assume the dimensions of the base are length (L) and width (W), and the height of the prism is H.
The perimeter of the base can be calculated using the formula: Perimeter = 2(L + W).
In this case, the perimeter is given as 10. So, we have:
10 = 2(L + W)
5 = L + W
Now, let's represent the number of lego cubes used for each dimension as L^3, W^3, and H^3.
Since the number of cubes used in each dimension is equal to its length (because each cube is 1 unit long on each side), we have:
L^3 + W^3 + H^3 = 222
We also know that the perimeter of the base is equal to 5. So, we can express one dimension in terms of the other:
L + W = 5
L = 5 - W
Substituting this into the equation for the number of cubes:
(5 - W)^3 + W^3 + H^3 = 222
We can now solve for the height, H.