We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website.
Please click on "Accept cookies" if you agree to the setting of cookies. Cookies that do not require consent remain unaffected by this, see
cookie policy and privacy policy.
DECLINE COOKIES

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