Question native Brooklyn, a student:

Is over there a method to uncover the perimeter the a rectangle if you have actually the area, or angry versa? If so, what is the equation?

We have actually two responses for you

Hi Brooklyn,

Suppose you have 4 feet of snapshot frame material and you desire to make a framework for among your photos. You could make a structure for your photograph of aunt Martha and also uncle Fred"s new baby.

You are watching: Is there a relationship between area and perimeter


or you might make a frame for a picture of her pet giraffe


or because that a photo you take it on your expedition to the mountains.


Each of these rectangles has the same perimeter, 4 feet, yet the areas are rather different. There is no direct relationship between the perimeter that a rectangle and also its area.


Hi Brooklyn, just knowing one piece of information, such together perimeter or area, is just not enough to recognize the exact dimensions of any type of rectangle. A rectangle that area 20 square units can have size of 2 x 10 or 4 x 5 or 1 x 20, etc. Every of this rectangles has actually a various perimeter (24 units, 18 units and 42 units respectively).

You would require to recognize a mix of any kind of two that the following: length, width, perimeter, area.

Obviously, if you understand the length and also width you"re set! You can calculate the perimeter making use of P=2L +2W and also you deserve to calculate the area making use of A = LW

If you understand the area and also either length or width, you have the right to use the area formula to recognize the other dimension: offered A = 24, l = 8 W = A/L W =24/8 W = 3. Currently you know both dimensions and you can determine the perimeter.

If you know the perimeter and also either length or width, you have the right to use the perimeter formula to determine the other dimension: given P = 40, together = 16 W = P/2 - together W = 40/2 - 16 W = 20 - 16 W = 4 now you know both dimensions and you deserve to determine the area.

If you know both the area and the perimeter, girlfriend can likewise determine the dimensions, however it bring away a little much more work and involves one of two people guessing and also checking (which may prove difficult or difficult if any type of dimension is irrational) or resolving a quadratic equation.

Given A = 15, p = 16 15 = LW 16 = 2L + 2W isolation the W, substitute right into the first equation and also solve. 16 - 2L = 2W 8 - l = W

15 = L(8 - L) 15= 8L - L2 move all state to one side and factor. L2 - 8L + 15 = 0 (L - 5)(L - 3) = 0 l - 5 = 0 together - 3 = 0 l = 5 together = 3

We would choose L = 5 (only since by convention us think that the length being the longer side) and by substitution right into one that our initial equations we find the broad is 3.

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Hope this helps, Leeanne

Math main is supported by the college of Regina and The Pacific Institute for the mathematical Sciences.