Question

如图所示,长方形纸片ABCD的长AD=9cm,宽AB=3cm,将其折叠，使点D与点B重合

求：（1）以折痕EF为边的正方形面积

Answer 1

设AE=X,ED=AD-AE=9-X;
AB²+AE²=BE²
BE=ED
3²+X²=(9-X)²
9+X²=81-18X+X²
X=72/18=4CM
BE²=3²+4²=25
BE=5CM=ED;
∠BEF=∠DEF=∠BFE,
BF=BE=5CM;
FC=BC-BF=AD-BF=9-5=4CM;
作EP⊥BC于P,
以折痕EF为边的正方形面积=EF²
=EP²+PF²
=AB²+(PC-FC)²
=3²+(ED-FC)²
=9+(5-4)²
=10(CM²)

Answer 2

设AE=X,ED=AD-AE=9-X;
AB²+AE²=BE²
BE=ED
3²+X²=(9-X)²
9+X²=81-18X+X²
X=72/18=4CM
BE²=3²+4²=25
BE=5CM=ED;
∠BEF=∠DEF=∠BFE,
BF=BE=5CM;
FC=BC-BF=AD-BF=9-5=4CM;
作EP⊥BC于P,
以折痕EF为边的正方形面积=EF²
=EP²+PF²
=AB²+(PC-FC)²
=3²+(ED-FC)²
=9+(5-4)²
=10(CM²)