What is the smallest parameter possible for a rectangle whose area is 16 square inches and what are it’s dimensions?

2 Answers
Jun 11, 2018

We get a=b=4

Explanation:

We have the Perimeter as

p=2(a+b)=2(a+16a)
So we get by AMGM

a+16a2a16a=8
Multiplying by 2

2(a+16a)416=16
the equal sign holds if
a=b=4

Jun 11, 2018

P=16

Explanation:

Let a=x inches be one side of the rectangle, then the other side is:

b=16x

measured also in inches.

The perimeter is then:

P=2(x+16x)

Evaluate the derivative:

dPdx=232x2

thus the derivative is null for x=4, and in this point the second derivative:

d2Pdx2=64x3>0

thus x=4 is a minimum.

We can conclude that the smallest perimeter is obtained when a=b=4, that is when the rectangle is a square.