if a rhombus is reshaped such that one of its diagonal increases by 5 % while other diagonal decreases by 5% find the percentage change in the area of Rhombus
Answers
Answer:
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 =
pq
2
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
The new length of the diagonal AC = q - q ×
4
100
= q - 0.04q = (1 - 0.04)q
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
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
% Change in area =
Change in area
The area of the rhombus
× 100
=
-0.0016pq
2
pq
2
× 100
= -0.16%
Thus, the area of the rhombus is decreased by 0.16%.
Step-by-step explanation: