jq find value in object where key matches a regex

In the JSON below, I need to find the value of the id key of every object where the value of state starts with "failed-"

[  {"id": "RA_kwDOGETrS84EmTf2","state": "uploaded"  },  {"id": "RA_kwDOGETrS84EmTf6","state": "failed-4325423"  },  {"id": "RA_kwDOGETrS84EmTf7","state": "uploaded"  }]

I got as far as extracting just the matching values of state:

.[] | .state | select(startswith("failed-"))

How do I find the corresponding values of id ?