Question

The length of each side of a square increases by 40%. By what percent does the area of the square increase?

Answer 1

Answer:

The area of the square increases by 96%

Step-by-step explanation:

Assume that the side of the square is x units

∵ The original side of the square = x

∵ The area of the square = side × side

∴ The original area of the square = x × x

∴ The original area of the square = x²

∵ The length of each side of a square increases by 40%

∴ The new side of the square = x + 40% × x

∴ The new side of the square = x + $\frac{40}{100}$ × x

∴ The new side of the square = x + 0.4x

∴ The new side of the square = 1.4x

→ Find the area of the new square

∴ The new area of the square = 1.4x × 1.4x

∴ The new area of the square = 1.96x²

→ Find the increase in the area

∵ The increase of area = new area - original area

∴ The increase of area = 1.96x² - x²

∴ The increase of area = 0.96x²

∵ The percentage of the increase = (increase ÷ original) × 100%

∴ The percentage of the increase in the area = $\frac{0.96x^{2}}{x^{2} }$ × 100%

∴ The percentage of the increase in the area = 96%

∴ The area of the square increases by 96%