Question:
If each of the dimensions of a rectangle is increased by 100%, then the area is increased by?
If each of the dimensions of a rectangle is increased by 100%, then the area is increased by?
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When the dimensions of a rectangle are increased by a percentage, the area increases by the square of that percentage. In this case, a 100% increase in both dimensions leads to a 300% increase in area.
Updated On: Mar 10, 2025
- 100%
- 200%
- 300%
- 400%
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The Correct Option is C
Solution and Explanation
We are given a rectangle with initial dimensions:
\[
\text{Old Length} = 100, \quad \text{Old Breadth} = 100
\]
So, the initial area is:
\[
\text{Area (Old)} = 100 \times 100 = 10,000
\]
Now, the new dimensions after a 100% increase are:
\[
\text{New Length} = 200, \quad \text{New Breadth} = 200
\]
So, the new area is:
\[
\text{Area (New)} = 200 \times 200 = 40,000
\]
The increase in area is:
\[
\text{Increase in Area} = 40,000 - 10,000 = 30,000
\]
Now, to calculate the percentage increase in area:
\[
\text{Percentage Increase} = \frac{30,000}{10,000} \times 100 = 300%
\]
Thus, the area is increased by 300%.
Final Answer: The correct answer is (c) 300%.
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