If a rhombus is re-shaped such that one of its diagonal increases by 4%, while other diagonal decreases by 4%. Find the percentage change in the area of rhombus.
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Step by Step Explanation:
Let's assume the length of the diagonals BD and AC of the rhombus ABCD are p and q respectively.
- The area of the rhombus =
- According to the question, one of its diagonal increases by 4%, while other diagonal decreases by 4%.
The new length of the diagonal BD = p + p × = p + 0.04p = (1 + 0.04)p
- The new length of the diagonal AC = q - q × = q - 0.04q = (1 - 0.04)q
- Now, the area of the rhombus =
|(1 + 0.04)p × (1 - 0.04)q|
= ...[Since, (a + b)(a - b) = a2 - b2]
- Change in area = New area of the rhombus - The area of the rhombus
- % Change in area =
|Change in area|
|The area of the rhombus|
= × 100
- Thus, the area of the rhombus is decreased by 0.16%.