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# geometry

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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
+13728
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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.

!

Dec 19, 2021
edited by asinus  Dec 19, 2021
#2
+13728
+1

If BD:CD = 1:2, then find AD.

$$\overline {AD}=h$$

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

$$h=\overline{AD}=6.08$$

!

Dec 19, 2021