Question

In rombul ABCD ,BD=24√2 cm si m(∡ADC)=120°.Calculati lungimea diagonalei AC si perimetrul rombului.

Answer 1

Daca  m(∡ADC)=120° => m(∡ADB)= m(∡BDC)=60° =>ΔADB si ΔBDC sunt echilaterale =>BD=DC=BC=24√2 cm
Daca AC∩BD={O} =>BO=OD=12√2 cm (diag. unui romb se injumatatesc si sunt perpendiculare)
In Δdr.DOC avem OC²=DC²-OD² sau OC²=1152-288 =>OC²=864 =>OC=12√6 cm =>diag.AC=24√6 cm
=>Aria=(24√6·24√2)/2=576√3 cm²
Perim.=4·24√2=96√2 cm