Electrified 6472

The electrified carpet was rectangular, 16 square meters in area, and no two points on it were more than 7 meters apart. What different circuits can carpets that meet these conditions have?

Correct answer:

o₁ =  18.5714 m
o₂ =  16 m

Step-by-step explanation:

$$\begin{gathered} S=16{\text{m}}^2 \\ S=ab \\ o=2(a+b) \\ a\le 7;b\le 7 \\ {a}_1=7\text{m} \\ {b}_1=S/7=16/7=\frac{16}{7}\doteq 2.2857\text{m} \\ {o}_1=2\cdot (a_1+b_1)=2\cdot (7+2.2857)=18.5714\text{m} \end{gathered}$$

$$\begin{gathered} a_2=\sqrt{S}=\sqrt{16}=4\text{m} \\ {b}_2=a_2=4\text{m} \\ {o}_2=2\cdot (a_2+b_2)=2\cdot (4+4)=16=16\text{m} \\ {o}_2\le o\le o_1 \\ 16\le o\le 18.571 \end{gathered}$$

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