Is the word pernas the same in Brazilian and European Portuguese?

Yes

The word "pernas" is identical in meaning, spelling, and grammar in both Brazilian and Continental Portuguese. The only difference is pronunciation. In Brazilian Portuguese, the vowels are more open and the rhythm is syllable-timed (each syllable has a similar duration). In Continental Portuguese, the vowels are often reduced or almost silent, and the rhythm is stress-timed. Furthermore, the final "s" in "pernas" is typically pronounced as an "s" [s] in most of Brazil (except in Rio de Janeiro), while in Portugal, it is almost always pronounced as a "sh" [ʃ] sound.

Brazilian Portuguese Examples

1. Minhas pernas estão muito cansadas hoje. (My legs are very tired today.)
2. Ele quebrou a perna jogando futebol. (He broke his leg playing soccer.)
3. Estou com as pernas geladas de tanto frio. (My legs are freezing from the cold.)
4. Ela tem pernas muito longas. (She has very long legs.)
5. Minhas pernas ficaram bambas com o susto. (My legs went weak from the scare.)

Continental Portuguese Examples

1. As minhas pernas estão muito cansadas hoje. (My legs are very tired today.)
2. Ele partiu a perna a jogar futebol. (He broke his leg playing soccer.)
3. Estou com as pernas geladas de tanto frio. (My legs are freezing from the cold.)
4. Ela tem pernas muito compridas. (She has very long legs.)
5. As minhas pernas ficaram trémulas com o susto. (My legs went shaky from the scare.)