# Honors Geometry

You work for a fencing company. A customer called, wanting to fence in his 1,320 square-foot rectangular garden. He ordered 148 feet of fencing, but you forgot to ask him for the width and length of the garden (these dimensions will determine some of the details of the order, so you need the information). You don't want the customer to think that you're incompetent, so you figure out the length and width from the information the customer has already given you. What are the dimensions? Hint, what is the area of the garden, and what is the perimeter of the garden? If you are having trouble using algebra to solve this problem, you may be able to get the answer through guess and check.

1. 👍
2. 👎
3. 👁
1. perimeter = 2 x + 2 y
where x is width and y is length
so 2 x + 2 y = 148
x + y = 74
also we know area = x*y = 1320
so
y = 1320/x
so
x + 1320/x = 74
x^2 + 1320 = 74 x
x^2 - 74 x = -1320
add (74/2)^2 = 37^2 =1369 to both sides
(x-37)^2 = 49
x = 37 +/- 7
x = 30 or x = 44
well, I think this garden is 30 by 44 feet

1. 👍
2. 👎
2. Thanks :) It is 30 by 44 feet :)

1. 👍
2. 👎

## Similar Questions

1. ### Calculus 1

A fence is to be built to enclose a rectangular area of 220 square feet. The fence along three sides is to be made of material that costs 6 dollars per foot, and the material for the fourth side costs 13 dollars per foot. Find the

2. ### Math

A fence is to be built to enclose a rectangular area of 310 square feet. The fence along three sides is to be made of material that costs 3 dollars per foot, and the material for the fourth side costs 14 dollars per foot. Find the

3. ### Math 115

A fence is to be built to enclose a rectangular area of 320 square feet. The fence along three sides is to be made of material that costs 6 dollars per foot, and the material for the fourth side costs 14 dollars per foot. Find the

4. ### Math

A fence is to be built to enclose a rectangular area of 310 square feet. The fence along three sides is to be made of material that costs 3 dollars per foot, and the material for the fourth side costs 14 dollars per foot. Find the

1. ### math

A rectangular field is to be enclosed on four sides with a fence. Fencing costs \$8 per foot for two opposite sides, and \$2 per foot for the other sides. Find the dimensions of the field of area 900 ft2 that would be the cheapest

2. ### Calculus

ABC Daycare wants to build a fence to enclose a rectangular playground. The area of the playground is 900 square feet. The fence along three of the sides costs \$5 per foot and the fence along the fourth side, which will be made of

3. ### Calculus

OPTIMIZATION PROBLEM: "A rectangular field is to be enclosed on four sides with a fence. Fencing costs \$7 per foot for two opposite sides, and \$5 per foot for the other two sides. Find the dimensions of the field of area 620ft^2

4. ### Math: Calculus

A fence is to be built to enclose a rectangular area of 230 square feet. The fence along three sides is to be made of material that costs 5 dollars per foot, and the material for the fourth side costs 15 dollars per foot. Find the

1. ### Math

For any circle, which ratio is equal to the number π? Select all that apply. ***A. Circumference ------------------- Diameter B. Circumference ------------------- Radius ***C. Circumference ------------------- 2 Times Radius D.

2. ### Calculus - Optimization

A fence is to be built to enclose a rectangular area of 800 square feet. The fence along 3 sides is to be made of material \$4 per foot. The material for the fourth side costs \$12 per foot. Find the dimensions of the rectangle that

3. ### Calculus

A rectangular lot adjacent to a highway is to be enclosed by a fence. If the fencing costs \$2.50 per foot along the highway and \$1.50 per foot on the other sides, find the dimensions of the largest lot that can be fenced off for

4. ### Math

I want to fence in a square vegetable patch. The fencing for the east and west sides costs \$5 per foot, and the fencing for the north and south sides costs only \$4 per foot. Find the total cost of the fencing as a function of the