题目内容
如图,在△ABC中,AD为∠BAC的平分线,DE⊥AB于E,DF⊥AC于F,△ABC面积是28cm2,AB=20cm,AC=8cm,则DE的长为______.
∵在△ABC中,AD为∠BAC的平分线,DE⊥AB于E,DF⊥AC于F,
∵DE=DF,
∴S△ABC=S△ABD+S△ACD=
AB•DE+
AC•DF,
∵△ABC面积是28cm2,AB=20cm,AC=8cm,
∴
×20DE+
×8DF=10DE+4DF=14DE=28,解得DE=2cm.
故答案为:2cm.
∵DE=DF,
∴S△ABC=S△ABD+S△ACD=
1 |
2 |
1 |
2 |
∵△ABC面积是28cm2,AB=20cm,AC=8cm,
∴
1 |
2 |
1 |
2 |
故答案为:2cm.
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