Posted by **Mathlete** on Tuesday, June 17, 2014 at 7:07pm.

A farmer wants to enclose a rectangular field with 180m of fencing. The side of the barn will act as one side of the enclosure, leaving 3 sides to be covered. The function that describes the area inside is f(x)=x(180-2x) what are the dimensions of the closure with the largest area?

- Functions -
**Damon**, Tuesday, June 17, 2014 at 7:21pm
180 x - 2 x^2 = A

2 x^2 -180 x = -A

x^2 - 90 x = - A/2

x^2 - 90 x + 45^2 = -A/2 + 45^2

(x-45)^2 = -(1/2) (A- 4050)

vertex at x = 45

so 45. 45 , 90

area = 4050

- Functions -
**Mathlete**, Tuesday, June 17, 2014 at 8:23pm
Thanks Damon! We got it now. We were stuck after line three so this was helpful.

- Functions -
**Damon**, Tuesday, June 17, 2014 at 8:39pm
Good, you are welcome

## Answer this Question

## Related Questions

Calculus - A farmer has 120 meters of wire fencing to make enclosures for his ...

math - A farmer plans to enclose a rectangular region, using part of his barn ...

calculus optimization problem - A farmer has 460 feet of fencing with which to ...

Pre calc - A farmer with 2000 meters of fencing wants to enclose a rectangular ...

math - Marķa plans to enclose a rectangular area of her yard using the 16-foot ...

Algebra - A farmer plans to enclose a rectangular region using part of his barn ...

math - Farmer Hodges has 50 feet of fencing to make a rectangular hog pen ...

Math - Farmer wants to enclose a rectangular area that is 600 sq. ft. He is ...

College Algebra - A farmer wants to build a rectangular fence using the side of ...

word problem - A farmer decides to enclose a rectangular garden, using the side...