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We have a triangle ABC and a point K on segment BC such that AK is an altitude to triangle ABC. If AK = 6, BK = 8, and CK = 7, and then what is the perimeter of the triangle?

 Dec 17, 2020
 #1
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We have a triangle ABC and a point K on segment BC such that AK is an altitude to triangle ABC. If AK = 6, BK = 8, and CK = 7, and then what is the perimeter of the triangle?

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Perimeter   P = √(62 + 82) + 15 + √(62 + 72)

 Dec 17, 2020
 #2
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Note that  we have two right triangles  formed  by  AK

One is  triangle BAK  and the other is CAK

BC  = BK + CK  =15

 

Usinfg the Pythagorean Theorem

 

BA   = sqrt ( BK^2 + AK^2)  =  sqrt  ( 8^2  + 6^2)  = sqrt ( 100)   =  10

And

CA  =sqrt ( CK^2  + AK^2)  =  sqrt ( 7^2 + 6^2)  =  sqrt (85)

 

So....the   perimeter is  BC + BA  + CA  =  15 + 10 sqrt (85)  =  15 + 10 sqrt (85)

 

 

cool cool cool

 Dec 17, 2020

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