A park is shaped like a rhombus and has area 96 sq m. If 40 m of fencing is needed to enclose the park, the cost, in INR, of laying electric wires along its two diagonals, at the rate of ₹125 per m, is
Correct Answer: 3500
Solution and Explanation
Area of the Rhombus:
The area of a rhombus is given by:
$ \text{Area} = \dfrac{1}{2} \times d_1 \times d_2 $
where $d_1$ and $d_2$ are the diagonals of the rhombus.
Step 1: Use the given area
Given: Area = 96
So,
$96 = \dfrac{1}{2} \times d_1 \times d_2$
$\Rightarrow d_1 \times d_2 = 96 \times 2 = 192$
Step 2: Use Pythagoras Theorem
Each half-diagonal forms a right-angled triangle with the side of the rhombus.
Given side of rhombus = 10 units.
Using:
$ \left( \dfrac{d_1}{2} \right)^2 + \left( \dfrac{d_2}{2} \right)^2 = 10^2 $
$ \Rightarrow \dfrac{d_1^2}{4} + \dfrac{d_2^2}{4} = 100 $
$ \Rightarrow \dfrac{d_1^2 + d_2^2}{4} = 100 $
$ \Rightarrow d_1^2 + d_2^2 = 400 $
Step 3: Use identity for square of sum
Using identity: $ (a + b)^2 = a^2 + b^2 + 2ab $
$ (d_1 + d_2)^2 = d_1^2 + d_2^2 + 2d_1d_2 $
Substituting values:
$ (d_1 + d_2)^2 = 400 + 2 \times 192 $
$ = 400 + 384 = 784 $
$ \Rightarrow d_1 + d_2 = \sqrt{784} = 28 $
Step 4: Cost of laying electric wires
Cost per meter = ₹125
Total length of wires = $d_1 + d_2 = 28$ meters
Total cost = $28 \times 125 = ₹3500$
Final Answer:
The total cost of laying electric wires along the diagonals is ₹3500.
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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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