SAT Math Practice II | Super English Test Challenge

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A small square region inside a larger square is shaded. The diagonal of the larger square is three times the diagonal of the small square in length. What fraction of the area of the larger square is not shaded?

$A small square region inside a larger square is shaded. The diagonal of the larger square is three times the diagonal of the small square in length. What fraction of the area of the larger square is not shaded?$

Let b be the side of the square and d the length of its diagonal.
Then, by Pythagoras theorem, d2 = b2 + b2 = 2 b2.

2/3

8/9

1/3

1/9

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