Question

如图,菱形ABCD的周长为16cm,∠DAB与∠ABC的度数之比为1:2,点O位对角线AC与BD的交点,求BD和AC的长

Answer 1

菱形abcd∠DAB与∠ABC互补,∠DAB与∠ABC的度数之比为1:2则 ∠DAB=60,∠ABC=120 因为菱形对角线垂直平分,且平分∠DAB与∠ABC故∠ADB=60,∠DAC=30,菱形ABCD的周长为16cm故ab=bc=cd=ad=4 三角形abd为等边三角形.BD=AB=4 RT△AOD中∠ADB=60A0=√3/2AD=2√3则,AC=2AO=4√3 BD=4,AC=4√3 (在60°的菱形中,短对角线等于边长,长对角线是短对角线的√3倍)