如图,已知菱形ABCD的周长为20cm,∠A:∠ABC=2:1,则对角线BD=_cm.

问题描述:

如图,已知菱形ABCD的周长为20cm,∠A:∠ABC=2:1,则对角线BD=______cm.

连接AC,交BD于点O,∵菱形ABCD的周长为20cm,∴AB=5cm,AD∥BC,AC⊥BD,∴∠BAD+∠ABC=180°,∵∠BAD:∠ABC=2:1,∴∠ABC=60°,∴∠ABD=30°,∴OA=12AB=52(cm),∴OB=AB2−OA2=523(cm),∴BD=2OB=53(cm...