Mathematics
In the adjoining figure, find the length of AD in terms of b and c.
![In the figure, find the length of AD in terms of b and c. Pythagoras Theorem, ML Aggarwal Understanding Mathematics Solutions ICSE Class 9.](https://cdn1.knowledgeboat.com/img/mla9/q6-c12-ct-pythagoras-ml-aggarwal-solutions-icse-class-9-1061x793.png)
Pythagoras Theorem
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Answer
In right angle triangle ABC,
By pythagoras theorem,
BC2 = AB2 + AC2
BC2 = c2 + b2
BC = .
From figure,
Area of △ABC = Area of △ABD + Area of △ADC
⇒ x AB x AC = x AD x BD + x AD x CD
⇒ (AB.AC) = (AD.BD + AD.CD)
⇒ AB.AC = AD.BD + AD.CD
⇒ AB.AC = AD(BD + CD)
⇒ AB.AC = AD.BC [∵ BD + CD = BC]
⇒ AD =
Putting values of AB, AC and BC in above equation we get,
AD =
Hence, AD = .
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