SOLUTION: How to calculate the maximum area of rectangle give the fixed perimeter of 24.
Algebra.Com
Question 1153651: How to calculate the maximum area of rectangle give the fixed perimeter of 24.
Found 3 solutions by Boreal, ikleyn, Alan3354:
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
length is x and width is 12-x, and that gives half perimeter of 12
area is x(12-x)
maximize their product, which is 12x-x^2
the vertex is at -b/2a or -12/-2 or x=6
12-x=6
This is a square with area 36 sq units
Calculus gets the same answer.
Answer by ikleyn(52786) (Show Source): You can put this solution on YOUR website!
.
Maximum area of a rectangle with given perimeter is the area of a SQUARE with this perimeter.
It is the general rule.
See the lessons
- HOW TO complete the square to find the minimum/maximum of a quadratic function
- Briefly on finding the minimum/maximum of a quadratic function
- HOW TO complete the square to find the vertex of a parabola
- Briefly on finding the vertex of a parabola
- A rectangle with a given perimeter which has the maximal area is a square
in this site.
So, in your case the perimeter is 24 units.
The square with such a perimeter has the side of 24/4 = 6 units,
and its area is 6*6 = 36 square units.
It is MAXIMAL possible area for rectangles with the perimeter of 24 units.
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
How to calculate the maximum area of rectangle give the fixed perimeter of 24.
------------
P = 2W + 2L = 24
W + L = 12
-----------------
1st try W = L = 6 and 6
Area = 6*6 = 36
Any changes --> Area = (W + c)*(W - c) = W^2 - c^2
Any value of c <> 0 ---> a smaller area.
RELATED QUESTIONS
The perimeter of a rectangle remains fixed at 16cm. By first writing, an equation... (answered by Boreal,ikleyn)
A carpenter is building a rectangle room with a fixed perimeter of 356 ft. What... (answered by Fombitz)
A carpenter is building a rectangle room with a fixed perimeter of 336 ft. What... (answered by Fombitz)
A carpenter is building a rectangle room with a fixed perimeter of 164 ft. What... (answered by Fombitz)
FIND THE DIMENSIONS OF A RECTANGLE WHOSE PERIMETER IS 76CM THAT WILL GIVE THE MAXIMUM... (answered by palanisamy)
how to find the maximum area of a rectangle if the perimeter is... (answered by rfer)
a fixed perimeter of 164ft, what dimensions would yield the maximum area? what is the... (answered by stanbon)
If the maximum area is 57cm with a fixed perimeter of 7 what is the... (answered by Alan3354)