Question

The triangle ABC has \(AB=24cm\). If D is on the line segment AC such that \(\widehat{ABC}=\widehat{BDC}\)and \(AD=7cm;DC=9cm\)then what is the length of BD?

Answer 1

Note: You must write your answer in English.

Answer 2

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Answer 3

We have \(\Delta CAB\sim\Delta CDB\left(g.g\right)\Rightarrow\dfrac{CB}{CD}=\dfrac{CA}{CB}\) \(\Rightarrow CB^2=CD\cdot CA\) We have \(CA=CD+DA=16\left(cm\right)\) \(\Rightarrow CB^2=9\cdot16=144\Rightarrow CB=12\left(cm\right)\) We have \(\dfrac{DB}{BA}=\dfrac{CB}{CA}=\dfrac{12}{16}=\dfrac{3}{4}\) \(\Rightarrow DB=\dfrac{3}{4}AB=18\left(cm\right)\)