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MaRussiya [10]
3 years ago
10

you have 160 yards of fencing to enclose a rectangular region. find the maximum area of the rectangular region

Mathematics
2 answers:
den301095 [7]3 years ago
3 0

I know that for a fixed perimeter, the shape that encloses the greatest area
is a circle, and the rectangle that encloses the greatest area is a square. 
Sadly, I don't know how to prove it to you without Calculus.

If you'll take my assertion that the greatest rectangle is a square, and accept
it on faith, then you should use your 160-yd of fence to enclose a square with
40-yd sides.  The area inside it is (40 x 40) = <em><u>1600 square yards</u></em><u>.</u>

Here are some other choices. 
Each one has the same perimeter ... 160 yards.
This table kind of suggests to you that a square is the rectangle
       with the greatest area.  (But it doesn't prove it.)

<u>Length</u>         <u>Width</u>         <u>Area</u>
  35-yd           45-yd         1,575 square yards              
  30                50              1,500
  25                55              1,375
  20                60              1,200
  15                65                 975
  10                70                 700
    5                75                 375
    3                77                 231
    2                78                 156
    1                79                   79
  2-ft           79-yd 1-ft           52.89
  1-ft           79-yd 2-ft           26.56
  1-inch      79-yd 35-in          2.19 square yards

With the same 160-yd of fence, you could have squeezed in some more
area by setting the fence down in a circle with circumference = 160-yd.
The area inside the circle would be

       Area = (pi) (radius)² = (circumference)² / (4 pi) = 2,037.2 square yards

The area of a circle is always (4 / pi) times the area of the square with the
same perimeter.  That's about 27.3% more area than the square.

777dan777 [17]3 years ago
3 0
To optimize the area, the shape should be a square.  Clearly, with 160 yards of fencing, the square will have side-length 160/4=40 yards.  Therefore, the area will be 40*40=1600 yards.
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Melissa is planning a rectangular vegetable garden with a square patch for tomatoes
astra-53 [7]

The expressions for the length and the width of the rectangular garden are <u>3x + 2 feet</u>, and <u>x + 5 feet</u> respectively where x is the length of the square patch for tomatoes.

A square is a quadrilateral with all four sides equal, and all four angles at 90°, whereas a rectangle is a quadrilateral with opposite pair of sides equal, and all four angles at 90°.

In the question, we are informed that Melissa is planning a rectangular vegetable garden with a square patch for tomatoes.

The side of the square is given to be x feet.

We are asked to write expressions for the length and width of the rectangular garden.

For the length of the rectangle:-

We are informed that she wants the length of the garden to exceed three times the length of the tomato patch by 2 feet.

Thus, the length of the garden can be shown as the expression <u>3x + 2 feet</u>.

For the width of the rectangle:-

We are informed that she also wants the garden's width to exceed the width of the tomato patch by 5 feet.

Thus, the width of the garden can be shown as the expression <u>x + 5 feet</u>.

Thus, the expressions for the length and the width of the rectangular garden are <u>3x + 2 feet</u>, and <u>x + 5 feet</u> respectively where x is the length of the square patch for tomatoes.

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The provided question is incomplete. The complete question is:

"Melissa is planning a rectangular vegetable garden with a square patch for tomatoes. She wants the length of the garden to exceed three times the length of the tomato patch by 2 feet. She also wants the garden's width to exceed the width of the tomato patch by 5 feet.

Let x represent the length, in feet, of the square tomato patch.

Write expressions to represent the length and width of Melissa's vegetable garden in terms of x.

Enter the correct answer in the box."

8 0
2 years ago
PLEASE HELP
KIM [24]
A20-a18=a1+19d-a1-17d=2d =281-97 so d=92
3 0
3 years ago
The double number line shows that 4 pounds of tomatoes cost $14. How much does it cost for 1 pound of tomatoes
Anton [14]

Answer:

3.5

Step-by-step explanation:

You would do 14 divided by 4.

1pound =3.5

4 0
3 years ago
Read 2 more answers
Write the name of the period that has the digits 486
kogti [31]
1.       <span>The name of period that has 486 in the given number which is 751 486  is hundreds.
period is considered to a group of places of the digits, like the given number 486 is the group of hundred because the highest number it contains is 400.
=> 400 + 80 + 6
=> 4 hundreds + 8 tens + 6 ones
=> 486
while 751 is the period of hundred thousands.
=> 700 000 + 50 000 + 1 000
=> 751 000

</span>
8 0
3 years ago
In the context of the passage, which "expression of art"
Ainat [17]

According to the given passage the most appropriate option is: C.

A single text produced by a previously unknown society.

<h3>Explanation:</h3>

In light of this passage's excerpt, we can infer that it would be most challenging to interpret a piece of art for which we have no context—that is, no understanding of its language, history, inflection, or society and culture.

<h3>The definition of a single text:</h3>

A single document that ties together the frequently disparate interests of parties involved in a conflict is used in a single-text negotiating strategy, a type of mediation.

<h3>What exactly is a paragraph?</h3>

1. A paragraph with only one brief sentence that clearly states the main idea.

2. A paragraph that consists of a single lengthy sentence that could support three, four, or five sentences.

To know more about  single text visit:

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