The length of a garden is three more than twice its width. If the area of the garden is 1,200 square feet, what is the perimeter of the garden. (An answer within 1 foot of the correct answer).

Hannah has 2000 feet of fence. She is going to make a rectangular garden using the fence and her barn for one side (so she only needs fencing on three sides of the garden). What is the largest area she can enclose? [Answer with just the number of square feet of area].

Guest Jul 10, 2018

#1**0 **

Let the width of the garden = W, then:

The length of the garden =2W + 3

Area = L x W

1,200 =W x (2W + 3)

W =23.756 - feet the width of the garden

2 x 23.756 + 3 =50.512 - feet the length of the garden

Perimeter = 2[L + W]

= 2[50.512 + 23.756]

=148.536

=~149 feet

Guest Jul 10, 2018

#2**+1 **

Hannah has 2000 feet of fence. She is going to make a rectangular garden using the fence and her barn for one side (so she only needs fencing on three sides of the garden). What is the largest area she can enclose? [Answer with just the number of square feet of area].

Let two equal sides of the fence = S

Then the remaining side (opposite the barn) is just 2000 - 2S

So....the area, A, is just

A = S (2000 - 2S) simplify

A = 2000S - 2S^2 take the derivative of this and set to 0

A' = 2000 - 4S = 0

Solving, we have

2000 - 4S = 0 add 4S to both sides

2000 = 4S divide both sides by 4

500 = S

So....the max area is S (2000 - 2S) = 500 ( 2000 - 2*500) = 500 (1000) = 500,000 ft^2

CPhill
Jul 10, 2018