Question

A farmer wants to make a rectangular field with a total area of 800m2. It is surrounded by a fence. It is divided into 3 equal areas by fences. What is the shortest total length of fence with which this can be done?

Answer 1

This is a rectangular field, it will have four fence in one direction, and two in the other. The vertical lines here are the same length on each other, likewise of the horizontal line.We can calculate the length of the fence from them as: 4V + 2H= L we also have three area added together come to 800: 3VH = 800 so, lets re-arrange that second equation H=800/3V And sub into the first: 4V + 1600/3V = L Multiply through by 3V: 12V^2+1600= 3LV Rearrange 12V^2 - 3LV+ 1600= 0 we have quadratic, lets take a look at discriminant with this quadratic discriminant= b^2 - 4ac discriminant= 9L^2 - 4*12*1600 discriminant= 9L^2 - 76800 the dicriminant must be positive so the following must be true 9L^2>=76800 L^2>=8533.33 L>=92.376 so 92.36 is answer