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The radius of the inscribed circle is 6 cm. What is the number of centimeters in the length of AB? Express your answer in simplest radical form.

 

 Jul 27, 2022
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The altitude of this triangle  drawn from  the right angle  to AB  =  6 + 6sqrt (2)

 

We have this relationship

 

(AB/ 2) /  (6 + 6sqrt (2))  =    (6 + 6sqrt (2))  / (AB  / 2 )      simplify

 

(AB/2)^2  =   (6 + 6sqrt (2) )^2

 

AB^2  / 4   =  ( 6 + 6sqrt (2) )^2

 

AB^2  =  4 ( 6 + 6sqrt (2))^2      take the square root of both sides

 

AB  = 2 ( 6 + 6sqrt (2)) =   12 ( 1 + sqrt (2) )

 

cool cool cool

 Jul 27, 2022

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