Respuesta :
If the numbers denoting the perimeter and area of the square are equal, the length of the diagonal will be 4√2 units.
What are Area and Perimeter?
An object's shape defines a region as its area. The area of a figure or any other two-dimensional geometric shape is how much space it takes up in a plane.
The whole length encircling a shape is referred to as its perimeter. Simply put, if a shape is stretched into a linear form, its perimeter is its length. In a two-dimensional plane, a shape's perimeter is the sum of its total dimensions.
Let the side of the square to be 'a'.
If Area and Perimeter of a square are equal then,
So, Area = Perimeter
a^2 = 4a
we get, a = 4 units.
Now, we can find the diagonal by using Pythagoras theorem,
We know that, Hypotenuse^2 = Base^2 + Perpendicular^2
Here, the hypotenuse will be the diagonal of the square.
So, We have,
Diagonal^2 = 4^2 + 4^2
= 16 + 16
= 32
∴ Diagonal = √32 = 4√2 units.
Learn more about Area and Perimeter from the link given below:
https://brainly.com/question/19819849
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