Help w/: How to find height, width and height from sidefaces on box in shape of rectangular prism

[atrick]

Ok, so the task I've been given is this:

A box has the shape of a rectangular prism. The side faces have areas of 96 cm², 252 cm², and 168 cm².
a What dimensions can the box have (length, width, and height)?
b How many liters of rice can fit in the box?

b is easy for me, but I don't understand how I'm gonna do challenge a.
been going around the internet but never find anyone who can help me ;(

 

[atrick]

found all like combinations for how every area can have been set togheter, but no idea how I'll transform that to finding the length, withd and height

 

[Dr.Peterson]

Ok, so the task I've been given is this:

A box has the shape of a rectangular prism. The side faces have areas of 96 cm², 252 cm², and 168 cm².
a What dimensions can the box have (length, width, and height)?
b How many liters of rice can fit in the box?

Have you tried writing an equation for each of the three facts, using variables for the unknown length, width, and height?

You could also use trial and error with the factors of the three numbers, but that will be harder (assuming you know enough algebra).

Show us anything you try, so we can see what help you need.