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.
+128406 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) )
