Question

How can you find the perimeter of a rectangle if you only know its area of it? The area of a rectangle 756 units squared. What is its perimeter?

Answer 1

Hint: In this question, we are given the area of a rectangle and we have to find its perimeter. For that, we first need to find the dimensions of the rectangle, that is, its length and the breadth. So, we assume the length and the breadth to be represented by some unknown variables x and y respectively. We can write the area in terms of these unknown quantities and then on rearranging the equation, we express one quantity in terms of the other and then find the perimeter.

Complete step by step answer:
Let the length of the rectangle be “x” and the breadth of the rectangle be “y”

We know that –
$
  area = length \times breadth \\
   \Rightarrow 756 = x \times y \\
   \Rightarrow y = \dfrac{{756}}{x} \\
 $
We also know that –
$
  perimeter = 2(length + breadth) \\
   \Rightarrow p = 2(x + y) \\
 $
Putting the value of y in the above equation, we get –
$
  p = 2(x + \dfrac{{756}}{x}) \\
  p = 2(\dfrac{{{x^2} + 756}}{x}) \\
 $
To find the perimeter of the given rectangle, we must know the value of both x and y, so we need 2 equations to solve this question but we have only one,
Hence the perimeter of the rectangle cannot be found using only the area.


Note: However, we can find the minimum perimeter of a rectangle from its area. As the measure of the two sides of a rectangle is different, so one side will always be greater than the other, thus the perimeter will be minimum when the two sides of the rectangle are equal.
Let \[x = y\]
$
   \Rightarrow 756 = {x^2} \\
   \Rightarrow x \approx 27.5 \\
 $
So, the minimum perimeter of the rectangle is $4(27.5) \approx 110$ .
To find the perimeter of a rectangle using the area, we must know one more relation between the sides of the rectangle.