在三角形ABC中，D和E分别是边AB和AC上的点，使得DE平行于BC。
如果AD = 2.5 cm，BD = 3.0 cm，AE = 3.75 cm，求AC的长度。

img src=/doubts_assets/images/158630-1605790744.png" style="width: 25%;">"

已知

在三角形ABC中，D和E分别是边AB和AC上的点，使得DE平行于BC。

AD = 2.5 cm，DB = 3 cm，AE = 3.75 cm。

要求

我们需要求AC的值。

解答

DE平行于BC（已知）

因此，

根据基本比例定理，AD/DB = AE/EC

2.5/3 = 3.75/EC

EC = (3.75 × 3) / 2.5

EC = 11.25 / 2.5

EC = 4.5 cm

从图中，

AC = AE + EC

AC = (3.75 + 4.5) cm

AC = 8.25 cm

AC的长度为8.25 cm。  

Tutorialspoint

更新于: 2022年10月10日

"&description=In a ABC D and E are points on the sides AB and AC respectively such that DE BC If AD 2 5 cm BD 3 0 cm and AE 3 75 cm find the length of AC img src doubts assets images 158630 1605790744 png style width 25 - Given:In a $Δ$ ABC, D and E are points on the sides AB and AC respectively such that DE $||$ BC.AD $=$ 2.5 cm, DB $=$ 3 cm and AE $=$ 3.75 cm.To do:We have to find the value of AC.Solution:DE $||$ BC (given)Therefore,By Basic proportionality theorem, $frac{AD}{DB}=frac{AE}{EC}$$frac{2.5}{3} =fr','sharer','toolbar=0,status=0,width=580,height=325');" href="javascript: void(0)" title="分享到 Facebook"> "&summary=In a ABC D and E are points on the sides AB and AC respectively such that DE BC If AD 2 5 cm BD 3 0 cm and AE 3 75 cm find the length of AC img src doubts assets images 158630 1605790744 png style width 25 - Given:In a $Δ$ ABC, D and E are points on the sides AB and AC respectively such that DE $||$ BC.AD $=$ 2.5 cm, DB $=$ 3 cm and AE $=$ 3.75 cm.To do:We have to find the value of AC.Solution:DE $||$ BC (given)Therefore,By Basic proportionality theorem, $frac{AD}{DB}=frac{AE}{EC}$$frac{2.5}{3} =fr','sharer','toolbar=0,status=0,width=580,height=325');" href="javascript: void(0)" title="分享到 LinkedIn">

47 次查看

开启你的职业生涯

完成课程，获得认证

立即开始