Answer:

or 
Step-by-step explanation:
Let:

Given


Solving (a): The polynomial for the volume in terms of height
Volume (V) is calculated using:


Expand

Open brackets


Rewrite as:

Solving (b): The dimensions when Volume = 180
Substitute 180 for V in: 

Rewrite as:

Factorize:


Express
as difference of two squares

This gives:



Since the height can not be negative, then H = 5 or H = 6
Recall that:


When H = 5


When H = 6


Hence, the dimensions of the box are:

or
