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
aliina [53]
1 year ago
15

A piece of wire 10 m long is cut into two pieces. One piece is bent into a square and the other is bent into an equilateral tria

ngle. (Round your answers to two decimal places.)
Mathematics
1 answer:
Luda [366]1 year ago
8 0

The maximum and the minimum total area inclosed are 6.25m² and 2.72m²

What is an area?

⇒ The area is the region bounded by the shape of an object.

Calculation:

Let x is the length of the piece of wire for the equilateral triangle, whose side will then be (x/3) m long.

⇒  (10 - x) = length of the remaining piece for the square, whose side will then be (10 - x)/4 m long.

h = height of the equilateral triangle = h = a×√3/2 = (x/3)×(√3/2)

(Where a is the side of the triangle)

A(x) = Total area of the square formed + Total area of the triangle formed

Then    A(x) = [(10 - x)/4]²+ (1/2)(x/3)(x/6)√3

                   = [(100 - 20x + x²)/16] +  (√3/36)x² .

           

The maximum total area enclosed :

⇒ The entire 10m length should be allocated to the square because a square produces more area per unit of its perimeter than does a triangle.

Thus if all square, then x=0 and A(0)  = [2.5]² = 6.25 m² = Maximumarea

If all triangle, then x = 10  and  A(10) = (1.732/36)(100) = 4.811 m² .

So, the maximum area occurs when it's all used to make a square of side 2.5 m.

The minimum total area enclosed is :

⇒ We want a relatively small square and a small triangle.

 We are going to Find x by setting the derivative of A(x) to zero.

d[ A(x)]/dx  =   [(-20 + 2x)/16] + (2√3/36)x = 0

                  =  -5/4  + (1/8)x  +  (√3/18)x  = 0

                 x =  5/[4 (1/8 + √3/18)]  = 5/[ 4(0.125 + 0.09622)] = 5/(0.88489)  ⇒5.65 m perimeter of the triangle                  

             

and (10 - x) = 4.35 = perimeter of square

And  

A(5.65) = [4.35/4]² +  (√3/36)(5.65)²

             = 1.1827 from the square+1.5358 from the triangle

             =  2.719m² total area = Minimum area

⇒ On rounding off it will be 2.72m²

Hence the maximum and the minimum areas are 6.25m² and 2.72m²

Learn more about the area here:

brainly.com/question/25292087

#SPJ1

Disclaimer: The question was given incomplete on the portal. Here is the complete question.

Questions:  A piece of wire 10m long is cut into two pieces. one piece is bent into a square and the other is bent into an equilateral triangle. How should the wire be cut so that the total area enclosed is a. a maximum? b. minimum?

You might be interested in
What is the percent change of $15.60 to $11.70?
Rashid [163]

Answer:

percentage change=25% .

Step-by-step explanation:

Given : $15.60 to $11.70    .

To find:  What is the percent change .

Solution: We have given that   $15.60 to $11.70  .

Change = final value - initial value .

Change   = $15.60 - $11.70  

                   =$3.9

percentage change = \frac{change}{original value}*100

                                =   \frac{3.9}{15.60}*100

                                =   \frac{390}{1560}*100.

On dividing both number by 3

percentage change=\frac{130}{520}*100.

percentage change=\frac{1}{4}*100.

percentage change=25% .

Therefore, percentage change=25% .

5 0
3 years ago
Read 2 more answers
For the function f(x)=(7-8x)^2, find f^-1 determine whether f^-1 is a function
sertanlavr [38]
Is this question correct ?

5 0
3 years ago
Please help As soon as possible!
True [87]

Answer:

10

Step-by-step explanation:

To find the area of a parallelogram you need to use the expression A = bh

When you plug that in it will be 120 = 12b

After this, you need to solve (10)

7 0
3 years ago
Read 2 more answers
What is the common ratio of the geometic sequence whose second and forth terms are 6 and 54, respectively?
Luda [366]

Answer:

C

Step-by-step explanation:

The n th term formula of a geometric sequence is

a_{n} = a r^{n-1}

where a is the first term and r the common ratio

Using the second and fourth term, then

ar = 6 → (1)

ar³ = 54 → (2)

Divide (2) by (1)

\frac{ar^3}{ar} = \frac{54}{6} = 9

r² = 9 ⇒ r = \sqrt{9} = 3 → C

7 0
3 years ago
Read 2 more answers
Mary’s coffee shop borrowed $9,850 for new chairs and tables. The money was borrowed for 9 months at 9 ¼ % discounted rate, what
Greeley [361]
Let
M---------------> money borrowed -------------> <span>$9,850
r--------------> </span>discounted rate--------> <span>9 ¼=9.25-------> 0.0925
t---------------> time--------> </span><span>9 months=9*30=270 days
D-------------> </span><span>amount of the discount

we know that
D=M*r*t/360=(9850)*(0.0925)*(270/360)=683.34

the answer is $683.34</span>
6 0
3 years ago
Other questions:
  • What is 200 divided by 150
    12·1 answer
  • The temperature is 3C at sunrise. By noon ,the temperature changes by 5C. What could be the temperature at noon?
    7·1 answer
  • Which set shows some of the solutions to 4y&gt;12?
    6·1 answer
  • How many days would it take a construction loan of $548,048 to earn$50,000 exact interest at 9% interest rate?
    6·1 answer
  • If 5 pounds of broccoli cost is $12 then how much will 7 pounds of broccoli cost?
    7·2 answers
  • Simplify each expression by using the distributive property and combining like terms.
    11·2 answers
  • Need help with this geometry question
    15·1 answer
  • How would I find the range btw im only allowed a Ti-84 calculator So pls tell me how to solve this without using any stepbystep
    9·2 answers
  • Show all work to multiply quantity 2 plus the square root of negative 25 end quantity times quantity 4 minus the square root of
    8·2 answers
  • Help me please!!!!!!!
    8·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!