题目内容
如图,三角形ABC中,点D在AB上,BD=2AD,点E在BC上,BC=4BE,点F在AC上,AC=5CF,已知阴影三角形DEF的面积是25,那么三角形ABC的面积是______.
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如图,作AG⊥BC,DH⊥BC,
∵BD=2AD,
∴
=
=
,
∵S△BED=
BE×DH,S△ABC=
BC×AG,
∵BC=4BE,
∴S△BED:S△ABC=
,
同理,可得S△CFE:S△ABC=
,
S△AFD:S△ABC=
,
∴S△ABC=25÷(1-
-
-
)=60.
故答案为:60.
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∵BD=2AD,
∴
DH |
AG |
BD |
AB |
2 |
3 |
∵S△BED=
1 |
2 |
1 |
2 |
∵BC=4BE,
∴S△BED:S△ABC=
1 |
6 |
同理,可得S△CFE:S△ABC=
3 |
20 |
S△AFD:S△ABC=
4 |
15 |
∴S△ABC=25÷(1-
1 |
6 |
3 |
20 |
4 |
15 |
故答案为:60.
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