# Accelerated Algebra

it takes 80 feet of fencing to enclose your garden. According to your calculations,you will need 350 square feet to plant everything you want. Is your garden big enough? Explain your answer.
They gave a rectangle length=40-x and width= x
I asked my mom and she also got confused.So we are stuck.

1. 👍 0
2. 👎 0
3. 👁 1,061
1. so far, so good. The area of such a rectangle is

x(40-x) = 40x - x^2

You want

40x - x^2 >= 350
-x^2 + 40x - 350 >= 0

Now, the roots of this function are
12.9 and 27.1

Since it is a parabola opening down, y is positive for x between the roots. So, for any value of x between 12.9 and 27.1, the garden will be more than 350 ft^2.

Or, you could have examined the equation and noted that the vertex is at x=20, where there is maximum area. f(20) = 400, more than big enough.

Just for future reference, the maximum area possible for a rectangle of given perimeter is when the rectangle is a square. So, with 80 feet of fencing, the maximum area is 400 ft^2, in a 20x20 square. So, it should have been immediately clear that there was enough fencing to enclose 350 ft^2.

1. 👍 0
2. 👎 1

## Similar Questions

1. ### Calculus

A landscape architect wished to enclose a rectangular garden on one side by a brick wall costing \$60/ft and on the other three sides by a metal fence costing \$50/ft. If the area of the garden is 102 square feet, find the

2. ### Math

How much fencing is needed to enclose a circular pond with diameter 12.5 feet? A. 37.5 feet **? B. 19.625 feet C. 78.5 feet D. 39.25 feet

3. ### math

A gardener has 720 feet of fencing to fence in a rectangular garden. One side of the garden is bordered by a river and so it does not need any fencing.What dimensions would guarantee that the garden has the greatest possible area?

4. ### Math

Ed is planning to put up a rectangular garden with a fixed area of 120m^2. If the dimension of the garden have to be whole numbers,determine the dimension that will require the least amount of fencing materials to enclose the

1. ### math

arnold has 24m of fencing to surround a garden, bounded on one side by the wall of his house. what are the dimensions of the largest rectangular garden that he can enclose? how do i solve this question please help step by step

2. ### 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.

3. ### Math

Suppose that 32 feet of fencing is available to enclose a rectangular garden., one side of which will be against the side of a house. What dimensions of the garden will guarantee a maximum area?

4. ### geometry

A garden is in the shape of a rectangle 26 feet long and 35 feet wide. If the fencing costs \$5 a foot, what will it cost to place fencing around the perimeter of the garden?

1. ### Math

How Much fencing is required to enclose a circular garden whose diameter is 287 m?

2. ### Math

Marlene wants to enclose her circular vegetable garden with fencing to keep rabbits from eating the vegetables. If the diameter of her garden is 14 feet, how much fencing will she need to buy if fencing is sold by the linear foot?

3. ### Unknow

A man has a rectangular garden. One length of the garden lies along a patio wall. However the rest of the garden is enclosed by 32 feet of fencing. If the length of the garden is twice its width, what is the area of the garden.

4. ### Geometry

Ralph wants to put a fence around his rectangular garden. His garden measures 53 feet by 55 feet.The garden has a path around it that is 3 feet wide. How much fencing material does Ralph need to enclose the garden and path?