The length of a rectangular plot is increased by 50%, to keep its area unchanged, the width of the plot should be decreased by ______?
A) 29.87%
B) 33.33%
C) 22.22%
D) 19.5%
Answers
Answer:
The width of the plot should be decreased by 33.33% to keep the area unchanged.
Step-by-step explanation:
Let the length of the plot be l and the breadth of the plot be b.
When the length is increased by 50%, the new length = l + 50/100×l
= 150 l/100
The area of the rectangle is given by the product of length and breadth.
Thus, the old area of the rectangular plot = l×b
Given that the area has to remain the same on increasing the length. Thus the breadth has to be decreased.
The new breadth can be calculated as follows.
150l/100 × (new breadth) = l×b
New breadth = (l×b×100)/150l
= 2b/3
Therefore, the decrease in the width can be calculated by taking the difference between the old and new breadth.
i.e b - 2b/3 = b/3
= 0.3333 ≡ 33.33%
Thus, the width of the plot should be decreased by 33.33% to keep the area unchanged.
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