If the rectangular faces of a brick have their diagonals in the ratio 3: 2√3 :√15, then the ratio of the length of the shortest edge of the brick to that of its longest edge is
- √3 : 2
- 2 : √5
- 1 : √3
- √2 : √3
The Correct Option is C
Solution and Explanation
Let the edges of the brick be \( a, b, c \) such that \( a < b < c \).
We are given:
- \( a^2 + b^2 = 9 \quad \text{(1)} \)
- \( a^2 + c^2 = (2\sqrt{3})^2 = 12 \quad \text{(2)} \)
- \( b^2 + c^2 = (\sqrt{15})^2 = 15 \quad \text{(3)} \)
Adding all three equations: \[ (a^2 + b^2) + (a^2 + c^2) + (b^2 + c^2) = 9 + 12 + 15 = 36 \] \[ \Rightarrow 2(a^2 + b^2 + c^2) = 36 \Rightarrow a^2 + b^2 + c^2 = 18 \quad \text{(4)} \]
Now, subtracting Equation (1) from Equation (4): \[ c^2 = 18 - (a^2 + b^2) = 18 - 9 = 9 \Rightarrow c = 3 \]
Similarly, subtracting Equation (3) from Equation (4): \[ a^2 = 18 - (b^2 + c^2) = 18 - 15 = 3 \Rightarrow a = \sqrt{3} \]
Hence, the required ratio is: \[ \frac{a}{c} = \frac{\sqrt{3}}{3} = \frac{1}{\sqrt{3}} \]
Final Answer: \( \boxed{\frac{1}{\sqrt{3}}} \)
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In the dynamic realm of creativity, artists often find themselves at the crossroads between drawing inspiration from diverse cultures and inadvertently crossing into the territory of cultural appropriation. Inspiration is the lifeblood of creativity, driving artists to create works that resonate across borders. In a globalized era of the modern world, artists draw from a vast array of cultural influences. When approached respectfully, inspiration becomes a bridge, fostering understanding and appreciation of cultural diversity. However, the line between inspiration and cultural appropriation can be thin and easily blurred.
Cultural appropriation occurs when elements from a particular culture are borrowed without proper understanding, respect, or acknowledgment. This leads to the commodification of sacred symbols, the reinforcement of stereotypes, and the erasure of the cultural context from which these elements originated. It is essential to recognize that the impact of cultural appropriation extends beyond the realm of artistic expression, influencing societal perceptions and perpetuating power imbalances.- CAT - 2025
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