If each side of a square is increased by 40%, find the percentage change in its area.
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 96%
The area of a square is side × side, so when the side is multiplied by a factor, the area is multiplied by the square of that factor. A 40% increase multiplies the side by 1.4.
Each side becomes 140% of the original side \(a\): new side \(=1.4a\)
New area, the square of the new side: \((1.4a)^{2}=1.96a^{2}\)
Increase in area: \(1.96a^{2}-a^{2}=0.96a^{2}\), that is, 96% of the original area