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<span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri,sans-serif"><span style="line-height:150%"><span style="font-family:新宋体">如图，矩形</span></span><i><span lang="EN-US" style="line-height:150%"><span style="font-family:"Times New Roman","serif"">ABCD</span></span></i><span style="line-height:150%"><span style="font-family:新宋体">中，</span></span><i><span lang="EN-US" style="line-height:150%"><span style="font-family:"Times New Roman","serif"">AB</span></span></i><span style="line-height:150%"><span style="font-family:新宋体">＝</span></span><span lang="EN-US" style="line-height:150%"><span style="font-family:"Times New Roman","serif"">3</span></span><span style="line-height:150%"><span style="font-family:新宋体">，</span></span><i><span lang="EN-US" style="line-height:150%"><span style="font-family:"Times New Roman","serif"">BC</span></span></i><span style="line-height:150%"><span style="font-family:新宋体">＝</span></span><span lang="EN-US" style="line-height:150%"><span style="font-family:"Times New Roman","serif"">4</span></span><span style="line-height:150%"><span style="font-family:新宋体">，</span></span><i><span lang="EN-US" style="line-height:150%"><span style="font-family:"Times New Roman","serif"">EB</span></span></i><span style="line-height:150%"><span style="font-family:新宋体">∥</span></span><i><span lang="EN-US" style="line-height:150%"><span style="font-family:"Times New Roman","serif"">DF</span></span></i><span style="line-height:150%"><span style="font-family:新宋体">且</span></span><i><span lang="EN-US" style="line-height:150%"><span style="font-family:"Times New Roman","serif"">BE</span></span></i><span style="line-height:150%"><span style="font-family:新宋体">与</span></span><i><span lang="EN-US" style="line-height:150%"><span style="font-family:"Times New Roman","serif"">DF</span></span></i><span style="line-height:150%"><span style="font-family:新宋体">之间的距离为</span></span><span lang="EN-US" style="line-height:150%"><span style="font-family:"Times New Roman","serif"">3</span></span><span style="line-height:150%"><span style="font-family:新宋体">，则</span></span><i><span lang="EN-US" style="line-height:150%"><span style="font-family:"Times New Roman","serif"">AE</span></span></i><span style="line-height:150%"><span style="font-family:新宋体">的长是（　　）</span></span></span></span></span><br />
                                                                                                                                                          <img height="102" src="/uploads/meth/20210321/ceeb1755e41691b7c41fa4a7ec2c9005.png" width="131" />

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<span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri,sans-serif"><span style="line-height:150%"><span style="font-family:新宋体">解：如图所示：过点</span></span><i><span lang="EN-US" style="line-height:150%"><span style="font-family:"Times New Roman","serif"">D</span></span></i><span style="line-height:150%"><span style="font-family:新宋体">作</span></span><i><span lang="EN-US" style="line-height:150%"><span style="font-family:"Times New Roman","serif"">DG</span></span></i><span style="line-height:150%"><span style="font-family:新宋体">⊥</span></span><i><span lang="EN-US" style="line-height:150%"><span style="font-family:"Times New Roman","serif"">BE</span></span></i><span style="line-height:150%"><span style="font-family:新宋体">，垂足为</span></span><i><span lang="EN-US" style="line-height:150%"><span style="font-family:"Times New Roman","serif"">G</span></span></i><span style="line-height:150%"><span style="font-family:新宋体">，则</span></span><i><span lang="EN-US" style="line-height:150%"><span style="font-family:"Times New Roman","serif"">GD</span></span></i><span style="line-height:150%"><span style="font-family:新宋体">＝</span></span><span lang="EN-US" style="line-height:150%"><span style="font-family:"Times New Roman","serif"">3</span></span><span style="line-height:150%"><span style="font-family:新宋体">．</span></span></span></span></span><br />
<img height="130" src="/uploads/meth/20210321/91df3fc299eba7a5e4c79a0ada1c7ae3.png" width="132" /><br />
<span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri,sans-serif"><span style="line-height:150%"><span style="font-family:新宋体">∵∠</span></span><i><span lang="EN-US" style="line-height:150%"><span style="font-family:"Times New Roman","serif"">A</span></span></i><span style="line-height:150%"><span style="font-family:新宋体">＝∠</span></span><i><span lang="EN-US" style="line-height:150%"><span style="font-family:"Times New Roman","serif"">G</span></span></i><span style="line-height:150%"><span style="font-family:新宋体">，∠</span></span><i><span lang="EN-US" style="line-height:150%"><span style="font-family:"Times New Roman","serif"">AEB</span></span></i><span style="line-height:150%"><span style="font-family:新宋体">＝∠</span></span><i><span lang="EN-US" style="line-height:150%"><span style="font-family:"Times New Roman","serif"">GED</span></span></i><span style="line-height:150%"><span style="font-family:新宋体">，</span></span><i><span lang="EN-US" style="line-height:150%"><span style="font-family:"Times New Roman","serif"">AB</span></span></i><span style="line-height:150%"><span style="font-family:新宋体">＝</span></span><i><span lang="EN-US" style="line-height:150%"><span style="font-family:"Times New Roman","serif"">GD</span></span></i><span style="line-height:150%"><span style="font-family:新宋体">＝</span></span><span lang="EN-US" style="line-height:150%"><span style="font-family:"Times New Roman","serif"">3</span></span><span style="line-height:150%"><span style="font-family:新宋体">，</span></span></span></span></span><br />
<span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri,sans-serif"><span style="line-height:150%"><span style="font-family:新宋体">∴△</span></span><i><span lang="EN-US" style="line-height:150%"><span style="font-family:"Times New Roman","serif"">AEB</span></span></i><span style="line-height:150%"><span style="font-family:新宋体">≌△</span></span><i><span lang="EN-US" style="line-height:150%"><span style="font-family:"Times New Roman","serif"">GED</span></span></i><span style="line-height:150%"><span style="font-family:新宋体">．</span></span></span></span></span><br />
<span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri,sans-serif"><span style="line-height:150%"><span style="font-family:新宋体">∴</span></span><i><span lang="EN-US" style="line-height:150%"><span style="font-family:"Times New Roman","serif"">AE</span></span></i><span style="line-height:150%"><span style="font-family:新宋体">＝</span></span><i><span lang="EN-US" style="line-height:150%"><span style="font-family:"Times New Roman","serif"">EG</span></span></i><span style="line-height:150%"><span style="font-family:新宋体">．</span></span></span></span></span><br />
<span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri,sans-serif"><span style="line-height:150%"><span style="font-family:新宋体">设</span></span><i><span lang="EN-US" style="line-height:150%"><span style="font-family:"Times New Roman","serif"">AE</span></span></i><span style="line-height:150%"><span style="font-family:新宋体">＝</span></span><i><span lang="EN-US" style="line-height:150%"><span style="font-family:"Times New Roman","serif"">EG</span></span></i><span style="line-height:150%"><span style="font-family:新宋体">＝</span></span><i><span lang="EN-US" style="line-height:150%"><span style="font-family:"Times New Roman","serif"">x</span></span></i><span style="line-height:150%"><span style="font-family:新宋体">，则</span></span><i><span lang="EN-US" style="line-height:150%"><span style="font-family:"Times New Roman","serif"">ED</span></span></i><span style="line-height:150%"><span style="font-family:新宋体">＝</span></span><span lang="EN-US" style="line-height:150%"><span style="font-family:"Times New Roman","serif"">4</span></span><span style="line-height:150%"><span style="font-family:新宋体">﹣</span></span><i><span lang="EN-US" style="line-height:150%"><span style="font-family:"Times New Roman","serif"">x</span></span></i><span style="line-height:150%"><span style="font-family:新宋体">，</span></span></span></span></span><br />
<span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri,sans-serif"><span style="line-height:150%"><span style="font-family:新宋体">在</span></span><span lang="EN-US" style="line-height:150%"><span style="font-family:"Times New Roman","serif"">Rt</span></span><span style="line-height:150%"><span style="font-family:新宋体">△</span></span><i><span lang="EN-US" style="line-height:150%"><span style="font-family:"Times New Roman","serif"">DEG</span></span></i><span style="line-height:150%"><span style="font-family:新宋体">中，</span></span><i><span lang="EN-US" style="line-height:150%"><span style="font-family:"Times New Roman","serif"">ED</span></span></i><sup><span lang="EN-US" style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:"Times New Roman","serif"">2</span></span></span></sup><span style="line-height:150%"><span style="font-family:新宋体">＝</span></span><i><span lang="EN-US" style="line-height:150%"><span style="font-family:"Times New Roman","serif"">GE</span></span></i><sup><span lang="EN-US" style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:"Times New Roman","serif"">2</span></span></span></sup><span lang="EN-US" style="line-height:150%"><span style="font-family:"Times New Roman","serif"">+<i>GD</i></span></span><sup><span lang="EN-US" style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:"Times New Roman","serif"">2</span></span></span></sup><span style="line-height:150%"><span style="font-family:新宋体">，</span></span><i><span lang="EN-US" style="line-height:150%"><span style="font-family:"Times New Roman","serif"">x</span></span></i><sup><span lang="EN-US" style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:"Times New Roman","serif"">2</span></span></span></sup><span lang="EN-US" style="line-height:150%"><span style="font-family:"Times New Roman","serif"">+3</span></span><sup><span lang="EN-US" style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:"Times New Roman","serif"">2</span></span></span></sup><span style="line-height:150%"><span style="font-family:新宋体">＝（</span></span><span lang="EN-US" style="line-height:150%"><span style="font-family:"Times New Roman","serif"">4</span></span><span style="line-height:150%"><span style="font-family:新宋体">﹣</span></span><i><span lang="EN-US" style="line-height:150%"><span style="font-family:"Times New Roman","serif"">x</span></span></i><span style="line-height:150%"><span style="font-family:新宋体">）</span></span><sup><span lang="EN-US" style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:"Times New Roman","serif"">2</span></span></span></sup><span style="line-height:150%"><span style="font-family:新宋体">，解得：</span></span><i><span lang="EN-US" style="line-height:150%"><span style="font-family:"Times New Roman","serif"">x</span></span></i><span style="line-height:150%"><span style="font-family:新宋体">＝</span></span></span></span></span><img height="35" src="/uploads/meth/20210321/4e2d03ae1cd4d60f9c7a067ebf53b45e.png" width="13" /><span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri,sans-serif"><span style="line-height:150%"><span style="font-family:新宋体">．</span></span></span></span></span><br />
<span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri,sans-serif"><span style="line-height:150%"><span style="font-family:新宋体">故选：</span></span><i><span lang="EN-US" style="line-height:150%"><span style="font-family:"Times New Roman","serif"">C</span></span></i><span style="line-height:150%"><span style="font-family:新宋体">．</span></span></span></span></span>

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