Family - land

The Veselý family bought a plot of land measuring 30½ m by 26⅔ m. Before they start building, they want to fence it. How many metres of fencing do they need to buy if they leave 2⅞ m for the gate?

Final Answer:

x =  111 ¹¹⁄₂₄ = 2675/24 m

Step-by-step explanation:

$$\begin{gathered} a=30\frac{1}{2}=30+\frac{1}{2}=\frac{30\cdot 2+1}{2}=\frac{60+1}{2}=\frac{61}{2}=30.5\text{m} \\ b=26\frac{2}{3}=26+\frac{2}{3}=\frac{26\cdot 3+2}{3}=\frac{78+2}{3}=\frac{80}{3}\doteq 26.6667\text{m} \\ c=2\frac{7}{8}=2+\frac{7}{8}=\frac{2\cdot 8+7}{8}=\frac{16+7}{8}=\frac{23}{8}=2.875\text{m} \\ o=2\cdot (a+b)=2\cdot (\frac{61}{2}+\frac{80}{3})=\frac{343}{3}\doteq 114.3333\text{m} \\ x=o-c=\frac{343}{3}-\frac{23}{8}=\frac{2744}{24}-\frac{69}{24}=\frac{2744-69}{24}=\frac{2675}{24}=\frac{2675}{24}\text{m}=111\frac{11}{24}\text{m}=111.4583\text{m} \end{gathered}$$

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