Question

如图,折叠矩形纸片ABCD,使AD边与对角线BD重合,得折痕DG,若AB=2,BC=1,求AG的长.

Answer 1

设A折叠后落在BD上的A'点,AG=X,

A'G=AG=X,

BG=AB-AG=2-X,

BD²=AB²+AD²=AB²+BC²=2²+1²=5,

BD=√5；

∠GA'D=∠A=90°,

A'D=AD=1,

BA'=BD-A'D=√5-1,

BG²-A'G²=BA'²

(2-X)²-X²=(√5-1)²

X=(√5-1)/2.