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.

0.16% decrease

Step by Step Explanation:

1. Let's assume the length of the diagonals BD and AC of the rhombus ABCD are p and q respectively.
2. The area of the rhombus =
 pq 2

3. 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 ×
 4 100
= p + 0.04p = (1 + 0.04)p
4. The new length of the diagonal AC = q - q ×
 4 100
= q - 0.04q = (1 - 0.04)q
5. Now, the area of the rhombus =
 (1 + 0.04)p × (1 - 0.04)q 2

=
 (12 - 0.042)pq 2
...[Since, (a + b)(a - b) = a2 - b2]
=
 pq - 0.0016pq 2

6. Change in area = New area of the rhombus - The area of the rhombus
=
 pq - 0.0016pq 2
-
 pq 2

=
 pq - 0.0016pq - pq 2

=
 -0.0016pq 2

7. % Change in area =
 Change in area The area of the rhombus
× 100
=

 -0.0016pq 2

 pq 2

× 100
= -0.16%
8. Thus, the area of the rhombus is decreased by 0.16%.
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