if two squares have the same area of 2500 meters squared,when combined what is the perimeter?
A = s^2 (A is area, s is side of square)
2A = 2s^2 (for two squares)
2A= 2500
2s^2 = 2500
s^2 = 1250
s = square root of 1250
Perimeter = 4 s
To find the combined perimeter of two squares with the same area, we need to know the length of the sides of the squares.
Let's denote the side length of the first square as 'a' and the side length of the second square as 'b'. We're given that both squares have an area of 2500 square meters:
Area of the first square = side length × side length = a × a = 2500 m²
Area of the second square = side length × side length = b × b = 2500 m²
Since both squares have the same area, we can set up the following equation:
a × a = b × b
Taking the square root of both sides, we get:
√(a × a) = √(b × b)
a = b
Therefore, the side lengths of both squares are equal.
The perimeter of a square is given by the formula: 4 × side length.
So, the perimeter of each square is 4a, and when combined, the total perimeter would be the sum of the perimeters of both squares:
Total perimeter = 4a + 4a = 8a
Since both squares have the same side length (a = b), we can simplify the equation to:
Total perimeter = 8 × side length
Total perimeter = 8a
Therefore, the combined perimeter of two squares with the same area of 2500 m² is 8 times the side length of each square.