如图,已知平行四边形ABCD,对角线AC,BD相交于点O,平行四边形ABCD的周长是100㎝,△AOB与△BOC的

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  • ∵平行四边形ABCD的周长是100㎝.∴ 2( AB + BC )= 100∴ AB + BC = 50∵ 四边形ABCD是平行四边形,对角线AC,BD相交于点O∴ BD=2BO 又∵△AOB与△BOC的周长的和是122㎝∴ AB + AO + BO + BC + BO + CO = 122 AB + BC +( AO + CO )+( BO + BO )= 122AB + BC + AC + 2BO = 122∴ 50 + AC + BD = 122∴ AC + BD = 72又∵ AC :DB=2 :1 ∴ AC = 2BD ∴ 2BD + BD = 72 3BD = 72 BD = 24 (cm) 则 AC = 2BD = 2 × 24 = 48 (cm)答:AC和BD的长分别为48cm、24cm.