Question

Luis has a square pasture with a surface area of 1800 m² and is not fenced. In the center of the pasture there is a tree from which he ties his horse with a rope that reaches exactly to the corners of the pasture and allows the horse to surround the terrain.What is the maximum length of travel the horse can take when circling the tree?

Answer 1

Since it is a square pasture, we can conclude that each side is given by:

`\begin{gathered} A=l^2 \\ where\colon \\ 1800=l^2 \\ l=\sqrt[]{1800} \\ l=30\sqrt[]{2} \end{gathered}`

the maximum length of travel the horse can take when circling the tree is basically the length of the rope, the length of the rope can be found using the pythagorean theorem, so:

`\begin{gathered} d=\sqrt[]{(30\sqrt[]{2})^2+(30\sqrt[]{2})^2} \\ d=\sqrt[]{3600} \\ d=60m \end{gathered}`

the maximum length of travel the horse can take is 60m