Question

what could be the least perimeter of a rectangle of area 16 square please solve it step by step explanation​

Answer 1

Answer:

The minimum perimeter is 16in for equal sides of 4in.

Step-by-step explanation:

If we denote one side of the rectangle with a, and the other with b we can write, that:

a⋅b=16

so we can write, that b=16a

Now we can write perimeter P as a function of a

P=2⋅(a+16a)

We are looking for the smallest perimeter, so we have to calculate derivative:

P(a)=2a+32a

P'(a)=2+(−32a2)

P'(a)=2−32a2=2a2−32a2

The extreme values can only be found in points where P'(a)=0

P'(a)=0⇔2a2−32=0

2a2−32=0

xa2−16=0

×x..a2=16

××xa=−4ora=4

Since, length is a scalar quantity, therefore, it cannot be negative,

When