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WHAT Is the least perimeter of a rectangle with an area of 32 square feet?
Wiki User
∙ 11y ago
It would be a square with side = sqrt (32)
area = b x h = 32
bh = 32
b = 32/h
b + h = minimum
This is a a max -min prob if you know calculus
perimeter = p = b + h = 32/h + h
first derivative = 0 is max or min
dp/dh = 0 = -32/h^2 + 1
32 /h^2 = 1
h^2 = 32
h = sqrt 32
b = 32/h = 32/sqrt 32 = 32(sqrt 32)/32 =sqrt (32)
p = b + h = sqrt(32) + sqrt(32) = 2 sqrt(32) = 11.314 feet, minimum perimeter, a square with side sqrt(32) = 5.657 feet on a side
The least perimeter is a square of side sqrt 32 which is the same as sqrt (2 x 16) which is the same as 4 root 2 so the perimeter would be 4 times that, ie (16 root 2) which is just over 22 feet 7½ inches.
Wiki User
∙ 11y ago
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What it the least perimeter of a rectangle with an area of 32 square feet?
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