Question 524005
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