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If the side of a square is increased by 20%, what is the percentage increase in its area?
40%
44%
20%
48%
44%
Use the net percentage change formula x+y+100xyтАЛ directly for two-dimensional area changes.
Initial side of the square is increased by 20%
Net┬аIncrease=x+y+100x├ЧyтАЛ
Use the net percentage change formula x+y+100xyтАЛ directly for two-dimensional area changes.
Students often make the mistake of simply doubling the percentage to get 40% instead of accounting for area scaling in two dimensions.
Define Initial Values
Let the original side of the square be s, so the initial area is A1тАЛ=s2.
A1тАЛ=s2
Determine New Side and Area
The side is increased by 20%, making the new side 1.2s. The new area is A2тАЛ=(1.2s)2.
A2тАЛ=1.44s2
Calculate Percentage Increase
Find the percentage increase using the formula A1тАЛA2тАЛтИТA1тАЛтАЛ├Ч100%.
Percentage┬аIncrease=s21.44s2тИТs2тАЛ├Ч100%=44%
B is correct because the percentage increase in the area of the square is 44%.
This concept of percentage scaling applies to all 2D shapes like circles and rectangles where area depends on the square of linear dimensions.
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