# [Python 2], 63 bytes

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    lambda a:[len(`map(max,v)`[1::3].strip('0'))for v in zip(*a),a]

An unnamed function accepting a list of lists of integers (in `{0,1}`) which returns a list of integers, `[width,height]`.

**[Try it online!][TIO-jnt0kqje]** 

[Python 2]: https://docs.python.org/2/
[TIO-jnt0kqje]: https://tio.run/##lVJBDoIwELzzit7amtVQvTXRj0ATaoRIAoWUhqifRwoVQUBj99Dd6czsJtvybq6F2jfJMWwymZ8vEkkeZLEiUS5Lkssb1DQKGOcHsauMTkuCfUxpUmhUo1ShR4tsJAUpGouZuDIWJkHgAwO/i/YWwkOjA/bZhQBHZS53wrmEQReO5A/0PnPdvnSa9hob/RCujjjH/5zhVfU1G5l/WK6ZssV4S5dfp1aUd6Xdn7bLs0vkA6PUqTIo0u4XeG8Mb08YUEIsnwLCocLNEw "Python 2 – Try It Online"