ANSWER
[tex]x[/tex]= 9 [tex]in[/tex]
EXPLANATION
The volume of a rectangular prism is given by the formula,
[tex]V[/tex]= [tex]l[/tex] x [tex]b[/tex] x [tex]h[/tex]
We substitute the dimensions to obtain,
[tex]V[/tex]= 6 x 3 x 12 [tex]in^{3}[/tex]
The volume of the rectangular pyramid is,
[tex]V[/tex]= [tex]\frac{1}{3}[/tex] x 6 x 12 x [tex]x[/tex] [tex]in^{3}[/tex]
Equating the two values gives,
[tex]\frac{1}{3}[/tex] x 6 x 12 x [tex]x[/tex] = 6 x 3 x 12
We divide through by 6×12 to get,
[tex]\frac{x}{3}[/tex] = 3
We solve for x to obtain,
[tex]x[/tex] = 3 x 3
[tex]x[/tex] = 9 [tex]in[/tex]
Hope this helps! Happy Monday!
