What should the dimensions of her pasture be?

Question

) A rancher needs to enclose three sides of a rectangular pasture. If she has 100 yards of fence and needs to enclose 1050 sq. yds., what should the dimensions of her pasture be?

Answer 1

2x+y = 100 ......(1)

xy = 1050 ......(2)

From (1), y = 100 - 2x.

Plug in (2),

x(100 - 2x) = 1050

Collect all terms in one side,

2x^2 - 100x + 1050 = 0

/2, x^2 - 50x + 525 = 0

Factor,

(x-15)(x-35) = 0

x = 15 yards, y = 100-2x = 70 yards <==Answer 1

or

x = 35 yards, y = 100-2x = 30 yards <==Answer 2

 

Answer 2

Hey Abdi -- I'd cut 3 sections: 35, 35, 30 ==> encloses 3 sides of a 30x35= 1050 sq.yds. Regards :)

Answer 3

Let L be length of fence and W be width

2W + L = 100   --> L = 100 - 2W

WL = 1050

W *(100 - 2W) = 1050

100W -2W² = 1050

2W²  - 100W + 1050 = 0

W² - 50W + 525 = 0

(W -15) *( W -35) = 0

It looks like 15 yds. by 70 yds. or 35 yds. by 30 yds.