Abox has a volume of 546cm3 and a surface area of 422cm2. what are the length, width and height?

We know that the formula for the volume of a box is:



Where:
l = length
w = width
h = height

The formula of the surface area of a box is:


Based on the given we know the following:


and



If we factor out the given volume, you can come up with 3 numbers that will satisfy the surface area formula:



Let:
l = 6cm
w = 7cm
h = 13cm
     
Now let's try this on the surface area formula:






The answer is then:
l = 6cm
w = 7cm
h = 13cm

Any order would be fine.