a rectangular field is to be enclosed on four sides with a fence. fencing costs 5$ per foot two opposite sides, and 6$ per foot for the other two sides. find the dimensions of the feild of area 710ft

Length of cheaper side = x = 29.21 ft

Length of expensive side = y = 24.31 ft

Step-by-step explanation:

Let

Length of cheaper side = x

Length of expensive side = y

Total Cost = 5 (x + x) + 6 (y+y) =

Total Cost = 5 (2x) + 6 (2y)

Total Cost = 10x + 12y

we also know that

xy = 710ft square

so

y = 710 ft sq. / x

Putting this in total cost equation

Total Cost = 10x + 12 (710 ft sq. / x)

f (x) = 10x + (8,520 ft sq. / x) (cost = f (x)

f' (x) = 10 - (8,520 ft / x^2) (x>0)

0 + (8,520 ft / x^2) = 10

8,520 ft / x^2 = 10

x^2 = 8,520 ft / 10

(x^2) ^1/2 = (8,520 ft / 10) ^1/2

x = 92.3 / 3.16

x = 29.21 ft

As given

xy = 710ft square

Putting value of x in above equation

29.21 y = 710

y = 710/29.21

y = 24.31 ft