# The circumference

The circumference and width of the rectangle are in a ratio of 5: 1. its area is 216cm2. What is its length?

Result

a =  18 cm

#### Solution:

$S=216 \ \text{cm}^2 \ \\ S=ab \ \\ o:b=5:1 \ \\ 2(a+b):b=5:1 \ \\ \ \\ 2(a+b)=5b \ \\ 2a+2b=5b \ \\ 2a=3b=18 \ \text{cm} \ \\ \ \\ S=a(2/3a) \ \\ a=\sqrt{ 3/2 \cdot \ S }=\sqrt{ 3/2 \cdot \ 216 }=18 \ \text{cm} \ \\ b=2/3 \cdot \ a=2/3 \cdot \ 18=12 \ \text{cm} \ \\ \ \\ \text{ Correctness test: } \ \\ S_{1}=a \cdot \ b=18 \cdot \ 12=216 \ \text{cm}^2 \ \\ o=2 \cdot \ (a+b)=2 \cdot \ (18+12)=60 \ \text{cm}$

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