In the given triangle ABC, if the lengths of AD & DC are 3 units & 4

Question

In the given triangle ABC, if the lengths of AD & DC are 3 units & 4 units respectively, What is the length of BD ?

A.  \sqrt{7} 
B. 2 \sqrt{3} 
C.  2.5 
D.  5 
E.  \sqrt{3}

ccooley · Answer

The attachment with the image appears to have been deleted.

CareerGeek · Answer

Hi  ccooley

Fixed. Thank you

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sachinsavailable · Answer

4/ BD=BD/3

BD X BD= 12

BD=2 SQRT 3

Answer: B

nwMike · Answer

Nice! Is this from a known theorem? I went with the longer approach..

AB^2 - BD^2 = 3^2= 9 (1)
AB^2 + BC^2 = 7^2 = 49 (2)
BC^2 - BD^2 = 4^2 = 16 (3)

(1) - (2) + (3) = -2BD^2 = -24 <=> BD = \sqrt{12} = 2\sqrt{3}

sachinsavailable · Answer

nwMike

Please check below figure

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