Question

A rectangular prism and a triangular prism each have a volume of 210 cubic meters. find possible dimensions for each prism.

Answer 1

An interesting question! Let's take a look at the rectangular prism first.

[Rectangular Prism]
We know that the formula for the volume of a rectangular prism is:
volume = length * width * height

or more simply
V = L*W*H

All we know is that the volume is 210 cubic meters. We can choose whatever we want for the dimensions to force it to work! We're free to do what we want!
210 = L*W*H

I like 10, that's a nice number. Let's make L = 10.
210 = 10*W*H

Hmm... but now I need W*H to be 21 (think about it, make sure you get why I say that). Well, how about W = 7 and H = 3? That should work.
210 = 10*7*3

It checks! Possible dimensions for the rectangular prism are L = 10 meters, W = 7 meters, and H = 3 meters. There are many other choices of course, but this is a possible choice.

[Triangular Prism]
Same idea, different formula. For a triangular prism, the volume is
V = 1/2 * L*W*H

But the volume is still 210 cubic meters, so we just have
210 = 1/2 * L*W*H

So, one of our dimensions is going to be cut in half. Why don't we just double L to make up for it? 
210 = 1/2*(20)*W*H

And we can leave W and H the same
210 = 1/2*20*7*3

Check that it works! A possible choice is L = 20 meters, W = 7 meters and H = 3 meters.

We're done!