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来源：学生作业帮 编辑：作业帮 分类：数学作业 时间：2024/05/09 04:45:13
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1)
DA=CB=5,等腰梯形;
作DM垂直于AB,垂足M,AM=(AB-2DC)/2=(7-2)/2=3,
DM²=AD²-AM²=5²-3²,
DM=4,
正方形时,GE=HF=GF=EF=AB-2AE=7-2X,
RT△AEG∽RT△AMD,[AAA]
AE:AM=GE:DM
X:3=(7-2X):4
4X=21-6X,
X=2.1;
2)
AE:AM=GE:DM
AE:3=GE:4
GE=4AE/3,...(1)
SGEFH=SABCD/2=[(DC+AB)DM/2]/2=(1+7)4/4=8,
GE*EF=8
GE*(AB-2AE)=8,
GE(7-2AE)=8,
...(1)代入上式:(4AE/3)(7-2AE)=8
2AE²-7AE+6=0
(2AE-3)(AE-2)=0
AE=3/2,或AE=2
DA=CB=5,等腰梯形;
作DM垂直于AB,垂足M,AM=(AB-2DC)/2=(7-2)/2=3,
DM²=AD²-AM²=5²-3²,
DM=4,
正方形时,GE=HF=GF=EF=AB-2AE=7-2X,
RT△AEG∽RT△AMD,[AAA]
AE:AM=GE:DM
X:3=(7-2X):4
4X=21-6X,
X=2.1;
2)
AE:AM=GE:DM
AE:3=GE:4
GE=4AE/3,...(1)
SGEFH=SABCD/2=[(DC+AB)DM/2]/2=(1+7)4/4=8,
GE*EF=8
GE*(AB-2AE)=8,
GE(7-2AE)=8,
...(1)代入上式:(4AE/3)(7-2AE)=8
2AE²-7AE+6=0
(2AE-3)(AE-2)=0
AE=3/2,或AE=2