Answer: 15 m
Step-by-step explanation:
Given
Total volume of the combined pyramid is [tex]V=2700\ mm^3[/tex]
Height of top and bottom pyramid is
[tex]h_t=16\ mm[/tex]
[tex]h_b=20\ mm[/tex]
If the base has a side length of x, its area must be [tex]x^2[/tex]
Volume of square prism is given by
[tex]\Rightarrow V=\dfrac{1}{3}Bh\quad [\text{B=base area}]\\\\\text{Total volume will be the sum of the two pyramids}\\\\\Rightarrow 2700=\dfrac{1}{3}\times x^2\times 16+\dfrac{1}{3}\times x^2\times 20\\\\\Rightarrow 2700=\dfrac{1}{3}\times x^2\times (16+20)\\\\\Rightarrow x^2=225\\\Rightarrow x=15\ mm[/tex]
Thus, the value of [tex]x[/tex] is 15 m.
