A rectangular field is to be enclosed on four sides with a fence. Fencing costs $4 per foot for two opposite sides, and $3 per foot for the other two sides. Find the dimensions of the field of area 650ft2 that would be the cheapest to enclose.

Step-by-step explanation:

 Lets suppose the one side be x and the other side of the rectangle be y

 given area

   implies x = 650/y

  Cost = 2*4*x+2*3*y=8x+6y

            = 8*650/y + 6y

            = 5200/y  + 6y

upon differentiating we get

          =

          = 2600/3

          y= = 43.3

           x= 15

C(43.3)= >0 hence it is a minima value

optimizing the result we get

Cost = 8*15+6*43.3 =$ 379.8

step-by-step explanation:

given that there are two triangles j'k'l' and jkl>

the former is got by dilating the second one.

when drawn on a grid, (graph paper) coordinates of vertices of first triangle is

(6,12)j, (9,6)k and (12,9)l

side jk has length = distance between j and k

=

side j'k'=distance between j' and k'

=

ie j'k'l' has sides 1/3 of that of corresponding sides of jkl.

hence scale factor of 1/3 is used to get j'k'l'from jkl