Answer:
The side length of the large square is √2 times larger than the side length of the small square.
Explanation:
Suppose we have a small square (square 1) and a large square (square 2). The area of the large square is twice that of the small square, that is,
A₂ = 2 A₁
A₂/A₁ = 2 [1]
The area of a square is equal to the length of the side (l) raised to the second power.
A = l²
l = √A
The ratio of l₂ to l₁ is:
l₂/l₁ = √A₂ / √A₁ = √(A₂/A₁)
We can replace [1] in the previous expression.
l₂/l₁ = √2
The side length of the large square is √2 times larger than the side length of the small square.