The areas of the two watch faces have a ratio of 16:25. What is the ratio of the radius of the smaller watch face to the radius of the larger watch face? What is the radius of the larger watch face?

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Answer 1 · 2016-12-03T16:32:16

5

#A_1 : A_2 = 16 : 25#

#A = pir^2#

#=> pir_1^2 : pir_2^2 = 16 : 25#

#=> (pir_1^2)/(pir_2^2) = 16/25#

#=> (r_1^2)/(r_2^2) = 4^2/5^2#

#=> r_1/r_2 = 4/5#

#=> r_1 : r_2 = 4 : 5#

#=> r_2 = 5#