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10. A triangle has sides

   

Find the length to one decimal place, of the perpendicular from the opposite vertex to the side whose length is

   

Vinay

Solution:

From the fig.

   

Then,

   

   

                                                             

   

This proves that ∆ABC is a right triangle, right angled at B.

Let BD be the length of perpendicular from B on AC.

So, area of ∆ABC = (BC x BA)/

   

[Taking BC as the altitude]

   

                                                       

   

Also, area of ∆ABC = (AC x BD)/

   

  [Taking BD as the altitude]

   

                                                       

   

BD

   

(to one decimal place)