Question

If each of the dimensions of a rectangle is increased by 100%, then the area is increased by?

• A. 100%
• B. 200%
• C. 300%
• D. 400%

Hint:

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.

Answer 1

The Correct Option is C

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%.