Question

11．如图，四边形ABCD是矩形，AB:AD = 4:3，把矩形沿直线AC折叠，点B落在点E处，连接DE，则DE:AC =

你好像错了耶 A．1:3 B．3:8 C．8:27 D．7:25 并说明为什么

Answer 1

过D做AC垂线交AC于F，过E做AC垂线交AC于G。设AB=4a，BC=3a，有AC=根号（3×3+4×4）=5a，S△ADC=S△ABC=S△AEC，∴有ABCD面积SABCD=S△ADC+S△ABC=2×S△AEC=2×S△ADC=2×1/2×AC×DF=AD×AB=12→DF=EG=2.4a，AF=根号（AD×AD-DF×DF）=1.8a，CG=根号（BC×BC-EG×EG）=1.8a，∴DE=AC-AF-CG=5a-1.8a-1.8a=1.4a∴DE：AC=1.4：5=0.28

Answer 2

1:2

Answer 3

选D

Answer 4

b