
∴∠B=∠C=∠ADE=60°,AB=BC,
∵∠ADB=∠DAC+∠C,∠DEC=∠ADE+∠DAC,
∴∠ADB=∠DEC,
∴△ABD∽△DCE,
∴
AB |
DC |
BD |
CE |
∵BD=4,CE=
4 |
3 |
设AB=x,则DC=x-4,
∴
x |
x−4 |
4 | ||
|
∴x=6,
∴AB=6,
过点A作AF⊥BC于F,
在Rt△ABF中,AF=AB•sin60°=6×
| ||
2 |
3 |
∴S△ABC=
1 |
2 |
1 |
2 |
3 |
3 |
故选C.
4 |
3 |
3 |
3 |
3 |
AB |
DC |
BD |
CE |
4 |
3 |
x |
x−4 |
4 | ||
|
| ||
2 |
3 |
1 |
2 |
1 |
2 |
3 |
3 |