river forms 1 side of 2 enclosures, 390 yds fencing avail.

[conner.katherine]

Hi, my algebra class gave me this problem.

a rancher needs to enclose two adjacent rectangualr corrals, one for cattle and one for sheep. if the river froms one side of the corrals and 390 yds of fencing is available, find the largest total area that can be enclosed.

I did this orginally (which is wrong)- 390/3= 130^2=16900 sq feet.
My teacher said the answer is 12000 something.
I just can't figure out how to even go about this problem. Length times width? But how do I know what they are?

 

[Loren]

Re: Need Help with a formula

Draw a sketch of the situation. You might have a horizontal line segment labeled y for length and three vertical segments, one at each end and one in the middle, each of which are labeled x. Can you build an equation that represents the amount of fencing which, of course, you know is 390 ft. Can you build another equation that tells the equality of the area. Now, if you solve the first equation for one of the variables, and substitute into the second equation, you will have an equation with Area on one side and an expression in one variable on the other side. Work with that to determine the maximum area. You didn't mention what process you are to use. Possibly graph it and determine the maximum point on the curve?

 

[Denis]

Re: Need Help with a formula

I did this orginally (which is wrong)- 390/3= 130^2=16900 sq feet.

But that gives you only 1 corral; you need 2 corrals:

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(river)
*             *             *
*             *             *
*             *             *
* * * * * * * * * * * * * * *

That's what Loren is telling you...