Boardroom rhymes with:
bedroom, headroom, backroom, ballroom, barroom, bathroom, bedroom, bridegroom, classroom, cloakroom, courtroom, darkroom, elbowroom, headroom, livingroom, lunchroom, mailroom, newsroom, playroom, restroom, schoolroom, stockroom, storeroom, sunroom, toolroom, washroom, workroom
Boardroom sounds like:
barthram, bartram, bertram, bertran, brethren