Question

[nguyen van minh]

cho tam giac ABC can tai A co canh day bang 14 cm, ke Ad la tia phan giac cua goc BAC( D thuoc BC). tinh do dai canh AB biet AD= 15cm

Answer 1

[Nguyễn Ngọc Linh]

Xét \(\Delta ABC\)cân tại \(A\left(gt\right):\)

\(\Rightarrow AB=AC\)

Xét \(\Delta ABD\)và \(\Delta ACD,:\)

\(\widehat{BAD}=\widehat{CAD}\left(AD:tpg\widehat{BAC}\right)\)

\(AB=AC\left(cmt\right)\)

\(AD\)chung 

\(\Leftrightarrow\Delta ABD=\Delta ACD\left(c.g.c\right)\)

\(+,\Rightarrow BD=CD\)( 2 cạnh t/ứ)

\(\Rightarrow D\)là trung điểm của \(BC\)

\(\Rightarrow BD=CD=\frac{BC}{2}=\frac{14}{2}=7\left(cm\right)\)

\(+,\Rightarrow\widehat{BDA}=\widehat{CDA}\)( 2 góc t/ứ)

Mà \(\widehat{BDA}+\widehat{CDA}=180^0\)

\(\Rightarrow2\widehat{BDA}=180^0\Leftrightarrow\widehat{BDA}=90^0\)

\(\Rightarrow\Delta ABD\perp\)tại \(D\)

\(\Rightarrow AD^2+BD^2=AB^2\left(Py-ta-go\right)\)

\(\Rightarrow15^2+7^2=AB^2\)

\(\Rightarrow AB^2=225+49\)

\(\Rightarrow AB^2=274\)

\(\Rightarrow AB=\sqrt{274}cm\)

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