Territory

In an old legend about the founding of Rome, it is said that Romulus and Remus could obtain for their city as much land as a single hide from a bull would cover. Romulus and Remus came up with a trick, they cut the hide into strips and with them bounded the land for the future Rome. Suppose that the hide had the shape of a rectangle with dimensions of 4 m and 2.5 m. What largest territory in the shape of a square could they delimit with the hide if they cut it into 2.5 mm narrow strips?

Final Answer:

S =  100 ha

Step-by-step explanation:

$$\begin{gathered} a=4\text{m}\to \text{mm}=4\cdot 1000\text{mm}=4000\text{mm} \\ b=2.5\text{m}\to \text{mm}=2.5\cdot 1000\text{mm}=2500\text{mm} \\ c=2.5\text{mm} \\ a\cdot b=c\cdot l \\ l=\frac{a\cdot b}{c}=\frac{4000\cdot 2500}{2.5}=4000000\text{mm} \\ {l}_1=l\to \text{m}=l:1000\text{m}=4000000:1000\text{m}=4000\text{m} \\ {l}_1=4x \\ x=l_1/4=4000/4=1000\text{m} \\ {S}_1=x^2=1000^2=1000000{\text{m}}^2 \\ S=S_1\to \text{ha}=S_1:10000\text{ha}=1000000:10000\text{ha}=100\text{ha}=100\text{ha} \end{gathered}$$

Try another example