Saturday

April 19, 2014

April 19, 2014

Posted by **susie** on Thursday, June 4, 2009 at 5:59pm.

A rancher wants to fence in an area of 2500000 square feet in a rectangular field and then divide it in half with a fence down the middle parallel to one side. What is the shortest length of fence that the rancher can use?

- math -
**Damon**, Thursday, June 4, 2009 at 6:47pmA = a b so b = A/a

P = 2 a + 3 b

P = 2 a + 3 A/a

now A=2.5*10^6

P = 2a + 7.5*10^6/a

dP/da = 0 at in or max

dP/da = 0 = 2 -7.5*10^6/a^2

a^2 = 3.75*10^6

a = 1.936*10^3

then b = 2.5*10^6/1.936*10^3

b = 1.291*10^3

P = 2*a+3*b = 7.745*10^3

**Related Questions**

CALC - A rancher wants to fence in an area of 1500000 square feet in a ...

Calculus - A rancher wants to fence in an area of 500000 square feet in a ...

Calculus - A rancher wants to fence in an area of 5189400 square feet in a ...

calculus - A rancher wants to fence in an area of 3000000 square feet in a ...

Calculus - A rancher wants to make an animal pen by fencing in an area of ...

Calculus-Applied Optimization Quiz Problem - A rancher wants to fence in a ...

math - mr.periwinkle owns a ranch.he wants to add an area in the shape of an ...

geometry - A rectangular field is 64 m X 25 m. Shawn wants to fence a square ...

Math - Jennifer plans to fence a rectangular area around her rectangular ...

Math - Jennifer plans to fence a rectangular area around her rectangular ...