Answered: A rectangle garden has a circumference…

Math

Calculus

A rectangle garden has a circumference of 80mm. What is the maximum possible area of the garden?

College Algebra

7th Edition

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter1: Equations And Graphs

Section: Chapter Questions

Problem 12T

See similar textbooks

Related questions

Q: The perimeter of an isosceles triangle is 38 m. Find the length of the sides of the triangle of…

A: Let's find.

Q: What are the dimensions of a rectangle with perimeter 160 cm and the maximum area' What is the…

A: Since you have posted multiple questions in this question which are not interlinked so I have solved…

Q: Find the maximum area of a rectangle circumscribed about a fixed rectangle of length 10cm and width…

Q: What is the maximum area of a rectangle that can be inscribed in a right triangle with a base 8 cm…

Q: A piece of wire 60 cm long is to be folded into a rectangle.what should be the dimensions so that…

Q: The top of a box is a rectangle with a perimeter of 72 inches. If the box is 8 inches high, what…

A: Given:The box (or cuboid) has the height 8 inches(i.e. h = 8 in.) and the perimeter of the top of…

Q: A farmer wants to fence a rectangular field and then divide it in half with a fence down the middle…

Q: Three pens of the same size are to be built along an existing fence. If 480 feet of fencing is…

Q: Find the maximum area of a rectangle with perimeter 8000 feet?

A: Let length of the rectangle= x feet Width= y feet So, perimeter= 2(x+y)=8000

Q: Find the length and width of a rectangle that has the given perimeter and a maximum area. Perimeter:…

Q: A man wants to construct a rectangular enclosure around his model railroad. Only three sides must be…

Q: Find the length and width of a rectangle that has perimeter 64 meters and a maximum area.

A: Given perimeter of rectangle is 64 meters. Let length of rectangle be x. Perimeter of…

Q: Find the length and the width of a rectangle that has perimeter 80 cm and a maximumarea

Q: A farmer would like to fence his rectangular lot on a river bank. If he has 800 m of fencing…

A: In the question consider the field as rectangular. Let h be height of rectangle and b be breadth of…

Q: Find the length and width of a rectangle that has the given perimeter and a maximum area.…

A: Let length, L of rectangle = (x) mLet width, B of rectangle = (y) m Perimeter of rectangle =…

Q: A farmer decides to enclose a rectangular garden, using the side of a barn as one side of the…

Q: A carpenter has a 10 foot long board to mark off a triangular area on the floor in the corner of a…

A: The carpenter has a 10 foot longboard in the corner of a room. We have to find the maximum area of…

Q: A rope of 40cm long is bent into the shape of a rectangle. Find the maximum rectangle area that can…

A: Let the length and breath of rectangle be l and b respectively. If a rope of length 40cm is bent in…

Q: A 20 feet wire is cut into two pieces. To form an isosceles triangle and a circle, find the…

A: Concept: If a solid is formed through a wire then the perimeter of the solid is equal to the length…

Q: What is the maximum volume of a square pyramid that can fit inside a cube with a side length of 14…

Q: What is the maximum area of a rectangle that can be inscribed in a right triangle with a base 8 cm…

A: The rectangle which can be inscribed in a right triangle with base 8 cm and height 6 cm.

Q: A rectangle has a perimeter of 40m. What could be the maximum area of the rectangle?

A: A rectangle has a perimeter of 40 m. Let x and y be the length and width of the rectangle. Now…

Q: A norman arch is a rectangle with a semicircle attached at one end. If you wish to make a window in…

Q: Find the length and width of a rectangle with perimeter 40 and maximum area. Length and width are?

A: Given: Perimeter of the rectangle is 40. To find: Length and width and maximum area of the…

Q: A rectangle is 7 cm longer than it is wide. Find the dimensions of the rectangle if its area is 337…

Q: A farmer wishes to enclose a rectangular region bordering a river, using 960 feet of fencing. What…

Q: A man wants to construct a rectangular enclosure around his model railroad. Only three sides must be…

A: Ans. Let the length of enclosure is x & width of enclosure is y

Q: what is the minimum perimeter that a rectangle with an area of 32 ft2 can have?

Q: 5. Find the maximum area of an isOsceles triangle whose perimeter is 18 inches.

A: 5) To find out the maximum area of an isosceles triangle whose perimeter is 18 inches.

Q: Building Play Area

Q: A rectangular lot having an area of 5000 sq. meters is to be fenced on three sides. Find the minimum…

A: Both these questions can be solved by applying the concept of maxima and minima.

Q: A rectangular building is to be built on a triangular corner lot with the perpendicular sides equal…

Q: A Norman window has the shape of a rectangle surmounted by a semicircle. (Thus the diameter of the…

A: Let's find.

Q: What is the maximum area of a rectangle that can be inscribed in a right triangle with a base 8 cm…

Q: A carpenter is building a rectangular room with a fixed perimeter of 392 ft. What dimensions would…

A: Let l & b be the length and breadth of the room

Q: what is the maximum possible volume of rectangle box with the sum of it is 12 edges 24cm

Q: A 20 feet wire is cut into two pieces. To form an isosceles triangle and a circle, find the…

Q: What is the maximum area that can be completed with 240 feet of fencing? What are the dimensions?

Q: A farmer has 20 feet of fencing, and he wishes to make from it a rectangular pen for his pig Wilbur,…

A: Let, width= x, length = y So, total fence needed= 2x+y=20 feet y= 20-2x

Q: When enclosing 3 sides, the maximum area for a given rectangular area is obtained by forming a…

A: Given:Length is twice the ?

Q: A square piece of green origami paper that is 6 inches on a side is being made into a gift box (with…

A: Maximizing the surface.

Q: A rectangular building is to be built on a triangular corner lot with the perpendicular sides equal…

Q: Find the length and width of a rectangle that has the given perimeter and a maximum area Perimeter:…

Q: Three sides of a trapezoid are 8 inches in length. How long must the fourth side be, so that the…

A: Given: Three sides of a trapezoid are 8 inches in length. Let the fourth side of trapezoid be 8+2x…

Q: A backyard pool has a concrete walkway around it that is 5 feet wide on all sides.The total area of…

Q: A fencing is limited to 50m length. What is the maximum rectangular area that can be fenced in using…

A: Recall: Area of rectangle=length*breadth

Q: Find the length and width of a rectangle that has the given perimeter and a maximum area. Perimeter:…

Q: find the lenght and width of a rectangle that has the given perimeter and a maximum area perimeter:…

A: We have to find the lenght and width of a rectangle that has the given perimeter and a maximum…

Q: A rancher has 1500 feet of fencing to enclose two adjacent rectangular corrals. What dimensions will…

A: Refer to the questionLet the common sides of two rectangular corrals be x then the sketch for the…

Question

A rectangle garden has a circumference of 80mm. What is the maximum possible area of the garden?

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Step by step

Solved in 4 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Area of a Circle$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

Similar questions

One side of a rectangle is 2 cm longer than a second side. If the area is 35cm2, find the dimensions of the rectangle.
A cylindrical container has a volume of 84 cubic inches and a radius of 3 inches. Find the height of the container.
A rectangular kitchen is 6 feet longer than it is wide and has an area of 112 square feet. Find the dimensions of the kitchen.
The area of a triangular church window is 90 square meters. The base of the window is 15 meters. What is the window’s height?
A beach tent is designed so that one side is open. Find the number of square feet of canvas needed to make the tent.
A garden has 60 yards of fencing and wants to enclose a rectangular garden that requires fencing only on three sides. Find the length and width of the plot that will maximize the area.
Mary Frances has a rectangular garden plot that encloses an area of 48 yd2. If 28 yd of fencing are purchased to enclose the garden, what are the dimensions of the rectangular plot?