Answer:
15 mm
Step-by-step explanation:
Since both pyramids are joined together, this means that the base of the pyramid which is a square have the same dimensions.
Let the length and width of the base be x, hence the dimension of the base is x mm by x mm.
For the first pyramid, the volume is:
V₁ = a²h₁/3; where a is the length of the square base, h₁ is the height.
Since the pyramid has a height of 16 mm, hence:
V₁ = 16x²/3
the second pyramid, the volume is:
V₂ = a²h₂/3; where a is the length of the square base, h₂ is the height.
Since the pyramid has a height of 20 mm, hence:
V₂ = 20x²/3
Since the total volume (V) of the pyramid is 2700 mm³, hence:
V = V₁ + V₂
V = 16x²/3 + 20x²/3
2700 = 16x²/3 + 20x²/3
2700 = 36x²/3
36x² = 8100
x² = 225
x = 15 mm
