Posted by Amy on Sunday, February 5, 2012 at 7:30pm.
A man has 340 yards of fencing for enclosing two separate fields, one of which is to be a rectangle twice as long as it is wide, and the other, a square. The square field must contain at least 100 square yards and the rectangular one must contain at least 800 yards.
(a.) If X is the width of the rectangular field, what are the maximum and minimum values of X?
(b.) What is the greatest number of square yards that can be enclosed in the two fields?
If you know how to answer even part of this question, that would be so helpful. Thank you so much :x :X

Calculus  Anonymous, Monday, February 6, 2012 at 12:18pm
the square has to be at least 10x10, using 40 yds of fence. That leaves 240 yds for the rectangle, so X+2X<=120, or X <= 40.
If X = 40, 2X = 80, so area = 3200
If 2X^2 = 800, X=20, so
20 <= X <= 40
As X increases from 20 to 40, the area increases from 800 to 3200
total area of square + rectangle can be as much as 3300
If the rectangle is 20x40, that uses up 120 yds of fence, leaving 220 for the square, or 55x55, with area 3025. Total area with maximum square is thus 3825.
Answer This Question
Related Questions
 calculus  a farmer has a 2040 ft of fencing and wishes to fence off two ...
 math  Flor is putting a fence around a field. The field is rectangular and ...
 Calculus  A wire 17 inches long is cut into two pieces. One piece is bent to ...
 math  if two square have the respective areas indicated in square yards,one ...
 Math  You have 300 meters of fencing with which to build two enclosures. One ...
 Calculus  you have 1000 yards of fencing and you plan to use the fencing to ...
 Calculus  you have 1000 yards of fencing and you plan to use the fencing to ...
 Math  Farmer has a field 1 square mile wide and 1 square mile wide. He divides ...
 8th Grade Math  Can you please check my answer? An American football field is a...
 Algebra 1  A landscaper has two gardens: one is a square and the other is a ...
More Related Questions