The circumference

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

Correct answer:

a =  18 cm

Step-by-step explanation:

$$\begin{gathered} S=216{\text{cm}}^2 \\ S=ab \\ o:b=5:1 \\ 2(a+b):b=5:1 \\ 2(a+b)=5b \\ 2a+2b=5b \\ 2a=3b \\ S=a(2\mathrm{/}3a) \\ a=\sqrt{3\mathrm{/}2\cdot S}=\sqrt{3\mathrm{/}2\cdot 216}=18\text{ cm } \\ b=2\mathrm{/}3\cdot a=2\mathrm{/}3\cdot 18=12\text{ cm } \\ \text{ Verifying Solution: } \\ {S}_1=a\cdot b=18\cdot 12=216{\text{cm}}^2 \\ o=2\cdot (a+b)=2\cdot (18+12)=60\text{ cm} \end{gathered}$$

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