Answer:
[tex]x=7.2[/tex]
Step-by-step explanation:
Let x represent height of the prism.
We know that volume of rectangular is equal to product of its height, width and length.
[tex]\text{Surface area of rectangular prism}=2(wl+lh+hw)[/tex], where w, h and l represents width, length and height respectively.
We have been given that the surface area of rectangular prism is equal to the volume of the prism. So we can set an equation as:
[tex]lwh=2(wl+lh+hw)[/tex]
We are also told that the measurements of the rectangular prism is 9 inches long and 4 inches wide. Upon substituting these values in above equation, we will get:
[tex]9\cdot 4\cdot x=2(4\cdot 9+9\cdot x+x\cdot 4)[/tex]
Let us solve for x.
[tex]36x=2(36+9x+4x)[/tex]
[tex]36x=2(36+13x)[/tex]
[tex]36x=2(36+13x)[/tex]
[tex]36x=72+26x[/tex]
[tex]36x-26x=72+26x-26x[/tex]
[tex]10x=72[/tex]
[tex]x=\frac{72}{10}\\\\x=7.2[/tex]
Therefore, the value of x is 7.2 inches.
