Question

矩形ABCD中,E,F,分别是BC,AD的中点,FG垂直于AE于点G,AB=6,BC=8,AE=2倍根号13

Answer 1

∵矩形ABCD,∴AD‖BC,∠B＝90°．∵FG垂直于AE,∴∠AGF＝90°,∴∠B＝∠AGF．∵AD‖BC,∴∠FAG＝∠BEA,∴△AFG∽△EAB,∴AF/AE＝FG/AB．∵F,分别是AD的中点,∴AF＝1/2AD．∵矩形ABCD,∴AD＝BC．∵BC=8,∴AD＝8,∴AF＝4,∴4/2√13＝FG/6,∴FG＝4√3.