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

 Nov 19, 2018
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         A

        

         6

 

B  8   K     6       C

 

 

Since AK is an altitude....we can use the Pythagorean Theorem here

 

AB  = √ [ BK^2 + AK^2 ]  =  √ [ 8^2 + 6^2]  = √100 =  10

 

And  AC  = √ AK^2 + KC^2 ]   =  √ [ 6^2 + 6^2] = √ [ 2 * 6^2 ]  = 6√2

 

So....the perimeter is

 

AB + BK + KC + AC   = 

 

10 + 8 + 6 + 6√2  =

 

24 + 6√2   units  ≈  32.49 units

 

 

 

cool cool cool

 Nov 19, 2018

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