Modeling the relationship between perimeter and area. Is there any equation that models the relationship between the area and perimeter of a rectangle?

atgnybo4fq

atgnybo4fq

Answered question

2022-11-18

Modeling the relationship between perimeter and area
Is there any equation that models the relationship between the area and perimeter of a rectangle?

Answer & Explanation

Taniyah Lin

Taniyah Lin

Beginner2022-11-19Added 14 answers

Step 1
The area is A = a b, while the perimeter is P = 2 ( a + b ). An exact relationship is of course impossible, but you can work out some inequalities. An example is shown below
( a b ) 2 0 implies that a + b 2 a b , therefore
( P / 4 ) 2 A
Step 2
I don't know how useful this can be, I guess it depends on the kind of problem you're working on.
trumansoftjf0

trumansoftjf0

Beginner2022-11-20Added 5 answers

Step 1
Depending on the elements of the rectangle that you know, you can have different relations. E.g., If you know a side a than: a ( p / 2 a ) = A where p is the perimeter and A the area.
Step 2
If you know the diagonal d you have: ( p 2 ) 2 2 A = d 2

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