What is the smallest perimeter possible for a rectangle whose area is 16in^2 and what are its dimensions? ...?

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22-11-2016
Mathematics

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What is the smallest perimeter possible for a rectangle whose area is 16in^2 and what are its dimensions? ...?

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MissPhiladelphia MissPhiladelphia · Answer 1 · 2016-11-23T08:46:45+01:00

MissPhiladelphia MissPhiladelphia

23-11-2016

Area of the rectangle is given as = 16 square inches
We know
Length * width = Area
Then
Width = Area/Length
Now
Perimeter = 2 (Length + Width)
Perimeter = 2[ {Length + (Area/Length)}]
Perimeter = 2[Length + (16/Length)]
When d(Perimeter)/d(length) = 0,
Then
2[Length + (16/Length)] = 0
Length + (16/Length) = 0
Length^2 + 16 = 0
(Length)^2 = -(4)^2
Then
Length = 4 inches
Now
Width = Area/Length
= 16/4
= 4 inches.

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