SOLUTION: find the dimensions of a rectangle area, which is to have perimeter of 100''. and which has maximum area
Algebra.Com
Question 524005: find the dimensions of a rectangle area, which is to have perimeter of 100''. and which has maximum area
Found 2 solutions by nerdybill, solver91311:
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
find the dimensions of a rectangle area, which is to have perimeter of 100''. and which has maximum area
.
Let x = width
and y = length
then, from perimeter
2(x+y) = 100
x+y = 50 (equation 1)
.
and, from area
area = xy (equation 2)
.
Solve equation 1 for y:
x+y = 50
y = 50-x
.
Substitute above into equation 2:
area = xy
area = x(50-x)
area = 50x-x^2
MAX is when:
x = -b/(2a)
x = -50/(2(-1))
x = -50/(-2)
x = 25 feet
.
substitute above into equation 1 to find y:
x+y = 50
25+y = 50
y = 25 feet
.
Max area is attained by a square measuring
25 ft by 25 ft
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
The dimensions of a rectangle with maximum area with a given perimeter is a square with sides that measure the perimeter divided by 4.
The perimeter of a rectangle is given by:
The area of a rectangle is given by:
Substituting from the perimeter equation:
 = w\left(\frac{P}{2} - w\right)\ \ \Rightarrow\ \ A(w) = \left(\frac{wP}{2} - w^2\right))
This function graphs to a parabola opening downward meaning that the vertex is a maximum. The maximum value of the function, hence the maximum area, is where the value of the first derivative is equal to zero:
 = A'(w) = -2w + \frac{P}{2})
Set equal to zero:
Hence, the maximum area rectangle for a given perimeter is a square with sides of length one-fourth of the perimeter.
John
My calculator said it, I believe it, that settles it
RELATED QUESTIONS
Find the dimensions of a rectangle of greatest area which has a fixed perimeter... (answered by Alan3354)
John has 300 feet of lumber to frame a rectangular patio (the perimeter of a rectangle is (answered by psbhowmick)
I am having a hard time understanding how to solve this problem.
John has 300 feet of... (answered by checkley71)
John has 300 feet of lumber to frame a rectangular patio (the perimeter of a rectangle is (answered by venugopalramana)
John has 300 feet of lumber to frame a rectangular patio (the perimeter of a rectangle is (answered by josmiceli)
John has 300 feet of lumber to frame a rectangular patio (the perimeter of a rectangle is (answered by checkley71)
4) John has 300 feet of lumber to frame a rectangular patio (the perimeter of a... (answered by checkley71)
4) John has 300 feet of lumber to frame a rectangular patio (the perimeter of a... (answered by funmath)
Could someone please help me with this. I just don't get algebra, but i'm getting better.
(answered by stanbon,jai_kos)
