Without pulling up the carpet (easy enough) try getting down on your hands and knees, rap your knuckles along the floor every foot of the width where the tank is to be located. You will hear the difference in sound as the rapping moves over the joists and the hollow space below. Note where you think the joists are located in the first row. Next, move over a foot or so, and then rap along a second row. If you hear or feel any solid sounds or rapping, that is where the floor joists run.
Don’t ask about the tank, if it is NOT in the lease, it is OK. Besides waterbeds, in my experience, pop far more often than tanks leak. (Fish, BTW, are NOT counted as pets either.)
Nonetheless, you can still get some 1x6s or 2x2s to distribute the weight, especially if it is NOT a wood stand. A wood stand does a very good job of distributing the weight over a floor. Run the boards perpendicular to the joists to create a tank stand pad.
I always put a $1 plastic “paint drop cloth†sheet under all my tanks â€"œ which your landlord should love to see. I cut the sheet back to the edge of the stand after I am done setting up, rearranging and stocking the tank.
A Glass gets brittle with age. I use a Styrofoam pad between the tank and the stand to even out the weight of the tank and help prevent stressing the glass. Six foam sheets are available in the insulation dept at Home Depot for $5.