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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? Correct Answer 8/9

ধরি Square - এর side b যেহেতু বড় square - এর কর্ণ ছোট square - এর তিনগুণ সেহেতু বড় square বাহুও ছোট square - এর তিনগুণ হবে। small square এর side b হলে তার area b2 ∴ larger " " " 3b " " " 9b2 ∴Unshaded area 9b2 - b2 = 8b2∴Fraction of the area = 8b29b2 = 89

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Simplify the value of $$\frac{{{\text{0}}{\text{.9}} \times {\text{0}}{\text{.9}} \times {\text{0}}{\text{.9 + 0}}{\text{.2}} \times {\text{0}}{\text{.2}} \times {\text{0}}{\text{.2 + 0}}{\text{.3}} \times {\text{0}}{\text{.3}} \times {\text{0}}{\text{.3}} - {\text{3}} \times 0.9 \times {\text{0}}{\text{.2}} \times {\text{0}}{\text{.3}}}}{{{\text{0}}{\text{.9}} \times {\text{0}}{\text{.9 + 0}}{\text{.2}} \times {\text{0}}{\text{.2 + 0}}{\text{.3}} \times {\text{0}}{\text{.3}} - 0.9 \times {\text{0}}{\text{.2}} - {\text{0}}{\text{.2}} \times {\text{0}}{\text{.3}} - 0.3 \times 0.9}} = ?$$
$$\frac{{38 \times 38 \times 38 + 34 \times 34 \times 34 + 28 \times 28 \times 28 - 38 \times 34 \times 84}}{{38 \times 38 + 34 \times 34 + 28 \times 28 - 38 \times 34 - 34 \times 28 - 38 \times 28}}$$            is equal to = ?
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