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
lukranit [14]
3 years ago
5

A rectangle has a perimeter of 30 ft. Find a function that models its area A in terms of the length x of one of its sides. What

side length, x, yields the greatest area. What is that area?
Mathematics
1 answer:
Vedmedyk [2.9K]3 years ago
6 0

Answer:

Step-by-step explanation:

Let the other side of the rectangle be y. The perimeter of the rectangle is expressed as P = 2(x+y)

Given P = 30ft, on substituting P = 30 into the expression;

30 = 2(x+y)

x+y = 15

y = 15-x

Also since the area of the rectangle is xy;

A = xy

Substitute y = 15-x into the area;

A = x(15-x)

A = 15x-x²

The function that models its area A in terms of the length x of one of its sides is A = 15x-x²

The side of length x yields the greatest area when dA/dx = 0

dA/dx = 15-2x

15-2x = 0

-2x = -15

x = -15/-2

x = 7.5 ft

Hence the side length, x that yields the greatest area is 7.5ft.

Since y = 15-x

y = 15-7.5

y = 7.5

Area of the rectangle = 7.5*7.5

Area of the rectangle = 56.25ft²

You might be interested in
Geometry i need help with this question pls help
Alexus [3.1K]

Answer:

X its X

Step-by-step explanation:

8 0
3 years ago
Which equation represents the line<br> 5x - y = 3 in slope-intercept form?
Nat2105 [25]

Answer:

y=5x-3

Step-by-step explanation:

7 0
3 years ago
William made 1/2 gallon of lemonade to divide equally among 3 people. How much lemonade will each person?
katovenus [111]
<span>a) 1/6 gallon all u need to do is divide</span>
8 0
3 years ago
Read 2 more answers
Solve 7 8 and 9 please
VLD [36.1K]
7) y = 4x
8) y = 7x/8
9) y = 25x/3

I think this are the answers.
7 0
3 years ago
Read 2 more answers
Need help asap please
Ivanshal [37]

Answer:

the answer is 11.7 because you round up the decimals

6 0
3 years ago
Other questions:
  • Anybody know the answer?
    5·1 answer
  • Which is the principal value of \sin^{-1}\left(0.43\right)sin −1 (0.43)sine, start superscript, minus, 1, end superscript, left
    11·1 answer
  • 6 divided by 2 over 3​
    6·2 answers
  • What is 0.267 rounded off to <br> 1 significant figure
    12·2 answers
  • What is the product ?
    7·1 answer
  • the perimeter of the rectangle is 120 feet. If the length of the rectangle is ten feet more than the width ,what are the dimensi
    15·1 answer
  • The triangles are similar what is the value of x? Enter your answer in the box
    9·1 answer
  • What are the next two numbers in this pattern?<br> 3, 6, 12, 24, . . .
    6·1 answer
  • Write an algebraic expression for the situation.
    7·1 answer
  • The graph shows the relationship between the number of gallons of fuel remaining in the tank of a semitruck and the number of mi
    8·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!