Question
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.
Answers
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
= x(20-2x)
= -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 + <b>25 - 25 </b>)
= -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
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
= x(20-2x)
= -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 + <b>25 - 25 </b>)
= -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
Related Questions
An 8 foot tall fence separates Larry's yard from Evan's yard.The fence is 3 feet from Larry's house...
A rectangular play area is to be fenced off in a person's yard and is to contain 108 yd^2. The next-...
A family wants to fence a rectangular play area alongside the wall of their house. The wall of their...
Ian wants to fence three sides of a rectangular exercise yard for his dog. The fourth side of the ex...