Answer :
Answer:
Step-by-step explanation:
Given
total Length of Fence is [tex]L=120\ m[/tex]
this length is divided to three square such that their area is minimum
suppose the side of three squares is x,y and z
Perimeter of squares
[tex]120=4x+4y+4z[/tex]
thus [tex]g(x,y,z)=4x+4y+4z[/tex]
thus [tex]g_x=4,g_y=4,g_z=4[/tex]
Total area [tex]A=x^2+y^2+z^2[/tex]
Thus [tex]f(x,y,z)=x^2+y^2+z^2[/tex]
[tex]f_x=2x[/tex]
[tex]f_y=2y[/tex]
[tex]f_z=2z[/tex]
Using lagrange's multiplying method we get
[tex]\Delta f=\lambda \Delta g[/tex]
[tex]<2x,2y,2z>=\lambda <4,4,4>[/tex]
[tex]2x=4\lambda[/tex] [tex]2y=4\lambda[/tex] [tex]2z=4\lambda [/tex]
thus [tex]2x=2y=2x[/tex]
[tex]x=y=z[/tex]
thus [tex]x=y=z=10[/tex]
so fence should be cut into equal parts of 40 cm each