# Calculus

posted by .

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 -

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.

## Similar Questions

1. ### math

Flor is putting a fence around a field. The field is rectangular and measures 9.38 yards (yd) long and 14.74 yd wide. How much fence must Flor purchase?
2. ### Algebra 1

A landscaper has two gardens: one is a square and the other is a rectangle. The width of the rectangular garden is 5 yards less than a side of the square one, and the length of the rectangular garden is 3 yards more than a side of …

Can you please check my answer? An American football field is a rectangle 120 yards long (including both end zones) and 53 1/3 yards wide. What is the area of an American football field?
4. ### calculus

a farmer has a 2040 ft of fencing and wishes to fence off two separate fields. one of the fields is to be a rectangle with the length twise as long os the width. while the other field is to be square. determine the dimension of the …
5. ### Calculus

you have 1000 yards of fencing and you plan to use the fencing to make 2 enclosures, one circular and one a square. How much of the 1000 yard of fencing should be used for each region if you want to maximize the combined area of both …
6. ### Calculus

you have 1000 yards of fencing and you plan to use the fencing to make 2 enclosures, one circular and one a square. How much of the 1000 yard of fencing should be used for each region if you want to maximize the combined area of both …
7. ### Math

You have 300 meters of fencing with which to build two enclosures. One will be a square, and the other will be a rectangle where the length of the base is exactly twice the length of the height. Give the dimensions of the square and …
8. ### math

if two square have the respective areas indicated in square yards,one with 25yards and the other 5 yards how many yards of fencing are needed to enclose the two regions
9. ### Calculus

A wire 17 inches long is cut into two pieces. One piece is bent to form a square and the other is bent to form a rectangle that is twice as wide as it is high. How should the wire be cut in order to minimize the total area of the square …
10. ### Math

Farmer has a field 1 square mile wide and 1 square mile wide. He divides it into fields 1/3 mile wide and 1/3 mile long how many fields will he have

More Similar Questions