1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
solniwko [45]
3 years ago
11

A rectangular area against a wall is to be fenced off on the other three sides to enclose 800 square feet. What are the dimensio

ns that is will result in the least amount of fencing?

Mathematics
1 answer:
zalisa [80]3 years ago
8 0

Answer:

The length of 20 feet and width of 40 feet will result in the least amount of fencing.

Step-by-step explanation:

Please find the attachment.

Let w represent width and l represent length of the rectangle.

We have been given that a rectangular area against a wall is to be fenced off on the other three sides to enclose 800 square feet.

We know that area of rectangle is width times length that is:

A=w\cdot l

800=w\cdot l This is our constraint equation.

We can see from the attachment that the fencing would be for 3 sides that is:

\text{Perimeter}=l+l+w

P=2l+w This is our objective equation.

From constraint equation, we will get:

w\cdot l=800

w=\frac{800}{l}

Substitute this value in objective equation:

P=2l+\frac{800}{l}

P=2l+800l^{-1}

Let us find the derivative of objective equation.

P'=2-800l^{-2}

Now, we will set the derivative equal to 0 to solve for length:

2-800l^{-2}=0

2-\frac{800}{l^2}=0

-\frac{800}{l^2}=-2

Cross multiply:

-2l^2=-800

\frac{-2l^2}{-2}=\frac{-800}{-2}

l^2=400

Take positive square root:

l=\sqrt{400}

l=20

Upon substituting l=20 in w=\frac{800}{l}, we will get:

w=\frac{800}{20}

w=40

Therefore, the length of 20 feet and width of 40 feet will result in the least amount of fencing.

You might be interested in
What is the nth term of the geometric sequence -2,10,-50
poizon [28]

Answer:

T_n=-1(-5)^n^-^1

Step-by-step explanation:

We are given;

A geometric sequence;

-2,10,-50

Required to determine the nth term

The nth term in a geometric sequence is given by the formula;

T_n=a_1r^n^-^1

where a_1 is the first term and r is the common ratio;

In this case;

a_1=-2

r = 10 ÷ -2

  = -5

Therefore;

To get the nth term in the given geometric sequence we use;

T_n=-1(-5)^n^-^1

Thus, the nth term is T_n=-1(-5)^n^-^1

3 0
3 years ago
7. A classroom has 7 blue chairs, 5 green
gizmo_the_mogwai [7]
If a chair is selected at random it would be blue because that’s the most chosen color
3 0
3 years ago
Read 2 more answers
Identify the property x + 3 = x + 3
lianna [129]

the answer is communicative

5 0
3 years ago
Read 2 more answers
One - eighth of 7.92 x 10^10
liraira [26]
The answer is 9900000000 (thats 8 zeros) What you do is you find 10^10 which is 10000000000 (ten zeros) and multiply that by 7.92 to get 79200000000 then you just multiply it by 1/8 to get the answer.
3 0
3 years ago
Please help with this questions. I’ve waisted over 100 points trying to get answers for one assignment just because the only peo
Scrat [10]
Y
-7
-4
-1
2
5

(X,Y)
(-2,-7)
(-1,-4)
(0,-1)
(1,2)
(2,5)
5 0
3 years ago
Other questions:
  • A security alarm requires a four-digit code. The code can use the digits 0–9 and the digits cannot be repeated. What is the appr
    12·2 answers
  • write an equation of a line in slope-intercept form if the slope is ½ and the y-intercept is -2. a. y = (½)x 2 b. x - 2y = -4 c.
    10·1 answer
  • Nnnnnnnnnnnnn nnnnnn nnnnn 
    12·1 answer
  • A recipe calls for 4 quarts popcorn and 3/4 grated cheese if you want to make 3/4 of that how much popcorn and grated cheese wil
    7·2 answers
  • 1/3x=5/12 show your work
    11·1 answer
  • Please help me find this
    9·1 answer
  • Help please?!!!!!!!!:8/8/&
    10·2 answers
  • Find the surface area of the composite figure
    7·2 answers
  • Bob is thinking about leasing a car. The lease comes with an interest rate of 8%. Determine the money factor that will be used t
    14·1 answer
  • Find the slope and the y-intercept of the graph of the linear equation. y=-7x+12<br><br>​
    12·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!