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In triangle ABC, AB = 17, AC = 8, and BC = 10. Let D be the foot of the altitude from C to AB. Find the area of triangle ACD. 

 Dec 12, 2020
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Semi-perimeter of  triangle   =  (17 + 8 + 10) / 2  =  35/2  = 17.5  =S

 

Let the sides  be A, B ,C

 

Area  =

 

sqrt   [ S ( S - A) (S - B) ( S - C)  ]    so we have

 

sqrt  [ 17.5  ( 17.5 -17) (17.5 - 10) ( 17.5 -8 ) ]  =

 

sqrt  [ 17.5 * .5  *  7.5  *  9.5 ]  =

 

sqrt   [ 623.4375  ] ≈ 

 

24.97 units^2

 

cool cool cool

CPhill Dec 12, 2020

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