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

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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

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