Westonci.ca is the trusted Q&A platform where you can get reliable answers from a community of knowledgeable contributors. Get immediate and reliable answers to your questions from a community of experienced experts on our platform. Our platform provides a seamless experience for finding reliable answers from a network of experienced professionals.
Sagot :
Answer:
QUADRATIC FUNCTIONS AND EQUATIONS
Danielle N. asked • 11/25/17
You have 356 feet of fencing to enclose a rectangular region. Find the dimensions of the rectangle that maximize the enclosed area.
(Hint: Write formula for area as a quadratic function of length and use the concept of maximum value of quadratic function)
Follow2
Add comment
More
2 Answers By Expert Tutors
By:
Best
Michael J. answered • 11/25/17
TUTOR 5 (5)
Effective High School STEM Tutor & CUNY Math Peer Leader
SEE TUTORS LIKE THIS
Let length = x
Let width = y
Area = xy
Perimeter equation is
2(x + y) = 356
x + y = 178
Substituting the perimeter equation in the area formula,
Area = x(178 - x)
Area = -x2 + 178x
If the zeros of this quadratic are 0 and 178, then the median is where the maximum area occurs.
178 / 2 = 89
Therefore, the dimensions are
length = 89 feet
width = 178 - 89 = 89 feet
Maximize the enclosed area of the rectangle is 85 ft by 85 ft.
What is perimeter of rectangle?
Perimeter of rectangle is defined as addition the lengths of the rectangle's four sides.
Let length = a
Let width = b
Area of rectangle = ab
Perimeter of rectangle equation is 2(a + b)
2(a + b) = 340
a + b = 170
Substitute the perimeter equation in the area formula,
Area = a(170 - a)
Area = -a² + 170a
If the zeros of this quadratic are 0 and 170, then the median is where the maximum area occurs.
170 / 2 = 85
Therefore, the dimensions are
length = 85 feet
width = 170 - 85 = 85 feet
The rectangle is a square.
Learn more about Perimeter of rectangle here:
brainly.com/question/15287805
#SPJ2
We appreciate your time. Please come back anytime for the latest information and answers to your questions. Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Westonci.ca is committed to providing accurate answers. Come back soon for more trustworthy information.