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In triangle ABC, AB = 10 and AC = 17. Let D be the foot of the perpendicular from A to BC. If BD:CD = 2:3, then find AD.

 Dec 18, 2021
 #1
avatar+13045 
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If BD:CD = 2:3, then find AD.

 

Hello Guest!

 

\((10^2-h^2):(17^2-h^2)=4:9\\ 900-9h^2=1156-4h^2\\ -5h^2=256\)

The specified ratio BD: CD = 2: 3 is not possible.

laugh  !

 Dec 19, 2021
edited by asinus  Dec 19, 2021
 #2
avatar+13045 
+1

 If BD:CD = 1:2, then find AD.

 

\(\overline {AD}=h\)

\((10^2-h^2):(17^2-h^2)=1:4\\ 400-4h^2=289-h^2\\ -3h^2=-111\\ h=\sqrt{37}\)

\(h=\overline{AD}=6.08\)

laugh  !

 Dec 19, 2021

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