# Math

posted by Ashlee

You want to build a garden around your garden. One side borders your house so it does not need a fence. If you only have 50m of fencing what dimensions should you make your garden in order to maximize the area?

1. Reiny

Let the side parallel to the house by y
the each of the other two sides be x
Make a sketch

2x + y = 50
y = 50-2x

area = xy
= x(50-2x)
=50x - 2x^2

the x of the vertex of this parabola is -b/(2a) = -50/-4 = 12.5

so x = 12.5
and y = 50-25 = 25

The garden should be 25 m long and 12.5 m wide

by Calculus:
area = 50x - 2x^2
d(area)/dx = 50-4x = 0 for a max of area
4x=50
x = 12.5
continue as above

## Similar Questions

1. ### algebra 1

Charles wants to build a vegetable garden such that three sides of the garden are fenced and the fourth side of the garden will be the existing back fence. He has 30 feet of fencing available. Find the dimensions of the garden that …
2. ### math

dale have decided to fence off the garden plot behind his house, using his house as a "fence" along one side of a garden, the lenght(which run parallel to the house)is e feet less than twice the width. Find the dimensions if 32feet …
3. ### Algebra 2

Ann wants to plant a rectangular garden next to a straight river. She has 120 feet of fencing and will not fence the side of the garden next to the river. What dimensions will produce the largest garden?
4. ### Polynomials and quadratic application

I want to make a rectangular garden by fencing in a area on the back of my house. Three sides of the rectangle will be fencing; the fourth side will be the side of the house. I have 60 feet of fence. What dimensions should I make the …
5. ### Maath:)

Sam is going to plant a rectangular flower garden next to his house. There will be a fence on three sides of the garden( fencing is not necessary along the houe). The area of the garden is to be 1,000sq. ft., and he has 90 feet of …
6. ### engineering mathematics 1

your father wants to fence a rectangular area in your backyard for a garden. one side of the garden is along rhe edgeof the yard is already fenced, so you only need to build a new fence along the other 3 sides of rectangle. if you …
7. ### Math

A rectangular garden is to be fenced by a farmer. One side of the garden is next to the wall of the house and need not to be fenced. Find the dimensions of the largest garden that can be enclosed with 100m of fencing.
8. ### Mathematics

Mary wants to build a fence around a rectangular area for a garden. She has 150 ft of fencing and she wants to leave 10 ft opening on side for a gate. In order to make a area of the garden. A maximum what should the dimensions of the …
9. ### Math

Chris wants to build a fence around his square garden. The garden measures 6 feet on each side. How many fencing material does he need?
10. ### math

3) You are fencing a rectangular puppy kennel with 25 ft of fence. The side of the kennel against your house does not need a fence. This side is 9 ft long. Find the dimensions of the kennel. 4) A gardener is planning a rectangular …

More Similar Questions