Question

If the diagonal of a square is 'a' units, what is the diagonal of the square, whose area is double that of the first square?

Answer 1

Let the sides of the first square be denoted by x

Therefore, x^2+x^2=a^2 by the Pythagorean theorem

2x^2=a^2

Therefore, the area of the first square is 0.5a^2

If the area of the second square is double that of the first square, the area of the second square is a^2.

Therefore, the sides of the second square has length a.

Therefore, the second square has diagonal of length (2×1/2)a=√2a^2