Posted by fifi on Monday, September 19, 2011 at 11:34am.
A rectangular play yard is to be constructed along the side of a house by erecting a fence on three sides, using house wall as the fourth wall. Find the demensions that produce the play yard of maximum area if 20 meters of fence is available for the project.
- math - Reiny, Monday, September 19, 2011 at 11:45am
Make a sketch,
let the width of the field be x,
let the length of the field be y
then y + 2x = 20 , (we need only one length)
y = 20-2x
area = xy
= -2x^2 + 20x
I don't know at what level of math-study you are.
If you know calculus, find
d(area)/dx = -4x + 20 = 0
x = 5 , then y = 10 for a max area of 50
If you don't know calculus, complete the square of the quadratic function
A = -2x^2 + 20x
= -2(x^2 - 10x + 25 - 25 )
= -2((x-5)^2 - 25)
= -2(x-5)^2 + 50
vertex is (5,50)
so the max area is 50 when x = 5 , as above
Answer this Question
More Related Questions
- Calculus 1 - A family wants to fence a rectangular play area alongside the wall ...
- Calc 1 - An 8 foot tall fence seperates Larry's yard from Evan's yard.The fence ...
- math - dale have decided to fence off the garden plot behind his house, using ...
- calculus - a farmer wishes to fence off a rectangular plot of land, using an ...
- Math Calculus - Three sides of a fence and an existing wall form a rectangular ...
- word problem? - A rectangular lot is to be bounded by a fence on three sides adn...
- math - Kira has feet of fencing. She will use it to form three sides of a ...
- Calculus 1 - You have 4L feet of fence to make a rectangular vegetable garden ...
- optimization calcus - A rectangular rose garden will be surrounded by a brick ...
- Math Algebra 2 - A rectangular garden is fenced on three sides with a wall ...