First of all you do not supply LED strips from a Transformer, you supply them from either a dedicated power supply or a Driver.
Its not possible for anyone to tell you exactly which one to buy as we do not know the rating of the LED strips you have.
You should buy a driver or power supply that has a bigger capacity than the total of both LED strips (The supplier of the strips should tell you the rating)
So for example
You buy a 2 Led strips each is 5 Watts / metre Each strip is 10m long 5 watts x 10 metres = 50 watts BUT you have two strips So 2 x 50 = 100 So you would want a power supply or driver that can provide 100 or more watts.
The power supply or driver also needs to be at the same voltage as the strips. Most probably the strips will be 12v, but do check
I will add to what has already been said, a driver is a current regulated power supply, it is used to supply a string of LED's wired in series, the voltage will vary according to how many LED's are used. Typical 320 mA output at 5 ~ 50 volt.
However simple power supplies are also labelled as drivers, in this case typical 10 VA at 12 volt. VA is nearly the same as watts, you can consider it as watts in most cases.
Most cheap LED strips are 12 volt, they have the driver (resistor) built in, since the white LED needs around 3 volt typical is 3 LED's and a resistor in series, then these groups are connected to each other in parallel all within the strip. Because of the resistor these strips have a very poor lumen per watt output, with colour changing often same as tungsten lighting, they are for decoration and are very pretty, but they are not designed for general lighting.
The type using a true driver i.e. current regulated are very different, and are designed for general lighting not simple decoration, lumen per watt the true driver type around 100 lumen per watt and the decoration type fixed voltage are around 50 lumen per watt, colour changing around 25 lumen per watt.
To compare a fluorescent tube 5 foot is around 85 lumen per watt with a wire wound ballast which have been discontinued and 95 lumen per watt with a HF electronic ballast, the LED tube replacement is around 100 lumen per watt if the old ballast is removed. A compact fluorescent in a bulb shape is around 60 lumen per watt and a LED in bulb shape around 75 lumen per watt.
The little spot lights are again with LED around 75 lumen per watt, but unless aimed at something to spread the light most of it is lost.
I think the LED strip is very good under cupboards above counter tops but in most other places it is too far away to light anything and is decoration only.
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