Question

The owner of a ranch has 1 , 700 1,700 yards of fencing material which to enclose a rectangular piece of grazing land along a straight portion of a river. If fencing is not required along the river, what are the dimensions of the pasture having the largest area

Answer 1

Answer:

x = 425 yard

y = 425 yard

Area  = 180625 square yard

Step-by-step explanation:

given data

fencing = 1,700 yards

solution

we consider here length and width is x and y

so parameter is = P

P = 2 ( x+ y)

1700 = 2 ( x+ y)  

x + y = 850    

x = 850 - y      ...............1

and

area of rectangle is

Area = x y

area = ( 850 - y  )  y

area = 850 y - y²

so for large area is

$\frac{dA}{dy}$  = 0

$\frac{dA}{dy}$ = 850 - 2y

so here

850 - 2y = 0

y = 425  yard

and from equation 1

x = 850 - y  

x = 850 - 425

x = 425 yard

and

Area = 425 × 425

Area  = 180625 square yard