Answer:
The height of the container is ![7x\ ft](https://tex.z-dn.net/?f=7x%5C%20ft)
Step-by-step explanation:
Let
L ------> the length of the rectangular container
W ----> the width of the rectangular container
H ---> the height of the rectangular container
we know that
The volume of the rectangular container is
------> equation A
we have
![W=x\ ft](https://tex.z-dn.net/?f=W%3Dx%5C%20ft)
![L=(x+0.5)\ ft](https://tex.z-dn.net/?f=L%3D%28x%2B0.5%29%5C%20ft)
![V=7x^{3}+3.5x^{2}](https://tex.z-dn.net/?f=V%3D7x%5E%7B3%7D%2B3.5x%5E%7B2%7D)
substitute the values in the equation A
![7x^{3}+3.5x^{2}=(x+0.5)(x)H](https://tex.z-dn.net/?f=7x%5E%7B3%7D%2B3.5x%5E%7B2%7D%3D%28x%2B0.5%29%28x%29H)
Factor the term x in the left side
![(7x^{2}+3.5x)(x)=(x+0.5)(x)H](https://tex.z-dn.net/?f=%287x%5E%7B2%7D%2B3.5x%29%28x%29%3D%28x%2B0.5%29%28x%29H)
Simplify
![(7x^{2}+3.5x)=(x+0.5)H](https://tex.z-dn.net/?f=%287x%5E%7B2%7D%2B3.5x%29%3D%28x%2B0.5%29H)
Factor the term 7x in the left side
![(7x)(x+0.5)=(x+0.5)H](https://tex.z-dn.net/?f=%287x%29%28x%2B0.5%29%3D%28x%2B0.5%29H)
Simplify
![(7x)=H](https://tex.z-dn.net/?f=%287x%29%3DH)
Rewrite
![H=7x\ ft](https://tex.z-dn.net/?f=H%3D7x%5C%20ft)