pvc board

Is it strong enough to epoxy to a boat and hold a transducer on a boat ?Not wanting to drill holes in the boat .

You wanting to do something like this?
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It's called transom saver

Stern saver . not the motor prop

I use a plastic cutting board I got at Dollar Store price $1 works great.

Yes it is

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I have used both a cutting board and another time pvc board. Both are strong enough, and cheap. Use 3M adhesive and you will be fine.