Question

Buna m-ati putea ajuta cu ceva....am rombul ABCD BD=12 raddical din 2 si m(<ADC)=120 de grade.Calculati Ac si P rombului

Answer 1

ABCD-romb, AC, BD-diagonale, BD=12√2cm, m( ADC )=120grade
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A=? P=?
A-ARIA ROMB, P-PERIMETRUL ROMBULUI
In tr AOD  drept in O OD=6√2cm, m(ung ODA)=60 grade, m(ung DAO)=30 grade,AD-ipotenuza⇒ AD=2*OD=2*6√2=12√2 cm, AO²=AD²-OD²=144*2-36*2=>AO=6√6cm⇒ BD=12√2cm,  AC=12√6 cm,
P=4*12√2=48√2 cm, A=AC*BD/2=12√6*12√2/2=144√3 cm²