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 cm2 S=ab o:b=5:1 2(a+b):b=5:1  2(a+b)=5b 2a+2b=5b 2a=3b=18 cm  S=a(2/3a) a=3/2⋅ S=3/2⋅ 216=18 cm b=2/3⋅ a=2/3⋅ 18=12 cm   Correctness test:  S1=a⋅ b=18⋅ 12=216 cm2 o=2⋅ (a+b)=2⋅ (18+12)=60 cmS=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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