# Rectangle - desc circle

Length of the sides of the rectangle are at a ratio 1: 3 . Radius of the circle circumscribed to rectangle is 10 cm. Calculate the rectangle's perimeter.

Correct result:

p =  50.6 cm

#### Solution:

$r = 10\ cm \ \\ a:b = 1:3 \ \\ 3a = b \ \\ \ \\ (2r)^2 = a^2 +b^2 \ \\ (2r)^2 = a^2 +(3a)^2 \ \\ 4r^2 = 10 a^2 \ \\ a = 4/10 r = 6.32455532034 \ cm \ \\ b = 3a = 18.973665961 \ cm \ \\ p = 2(a+b) = 50.6 \ \text{cm} \ \\$

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