Is it possible for two rectangles or squares to have the same area, but only if they have the same perimeter??
my first rectangle is 3 by 8 , so it has an area of 24
my 2nd rectangle is 6 by 4, so it has an area of 24
Are the perimeters of the two rectangles the same ?
yes! thanks!
To determine if two rectangles or squares can have the same area only if they have the same perimeter, we need to verify if there are any possible scenarios where this condition holds true.
Let's start with rectangles:
1. Consider two rectangles with different dimensions and the same area:
Rectangle 1: Length = 4, Width = 5, Area = Length x Width = 4 x 5 = 20
Rectangle 2: Length = 2, Width = 10, Area = Length x Width = 2 x 10 = 20
In this case, despite having different dimensions, both rectangles have the same area. However, the perimeters are different:
Perimeter of Rectangle 1 = 2(Length + Width) = 2(4 + 5) = 18
Perimeter of Rectangle 2 = 2(Length + Width) = 2(2 + 10) = 24
Therefore, it is evident that two rectangles can have the same area but have different perimeters.
Now let's consider squares:
2. Consider two squares with different dimensions (side lengths) and the same area:
Square 1: Side Length = 5, Area = Side Length x Side Length = 5 x 5 = 25
Square 2: Side Length = 2, Area = Side Length x Side Length = 2 x 2 = 4
In this case, despite having different dimensions, both squares have the same area. However, the perimeters are different:
Perimeter of Square 1 = 4 x Side Length = 4 x 5 = 20
Perimeter of Square 2 = 4 x Side Length = 4 x 2 = 8
Again, we can see that two squares can have the same area but different perimeters.
Therefore, it is not possible for two rectangles or squares to have the same area only if they have the same perimeter.