Posted by Madeline on .
A farmer needs to build a rectangular corral for his animals. He has 200 yards of fencing available. He needs to make 4 pens. What is the largest corral he can create? (Remember the pens also count as a part of the perimeter, not just the outside of the corral)

College Algebra 
Steve,
depends on the configuration of the pens. A longs skinny corral with 4 pens in a row? Or a rectangular corral with a 2x2 arrangement of pens?
If the first, then we have two lengths and 5 widths.
2x+5y = 200
area = xy = x(2002x)/5 = 2/5 x^2 + 40x
the vertex of the parabola is at x=40/(4/5) = 50
So, the corral is 50 by 25
If the pens are in a grid, then we have 2 length and 3 widths:
2x+3y = 200
area = xy = x(2002x)/3 = 2/3 x^2 + 200/3 x
The vertex is now at x=50, so the corral is 50 by 33.33
Looks like the squareish pen is bigger. 
College Algebra 
nicole,
write the equation for the line that passes through the point (4,7) and is perpendicular to 3y8=x4. leave equation in thw pointslope form show all work