Question

If one of the sides of a square is increased by 20% and the other side of decreased by 20% to get a rectangle, what percent of the area of the square will be the area of this rectangle?

• A. 96%
• B. 4%
• C. 60%
• D. None of these

Hint:

When one side of a square increases and the other decreases, the area is impacted by the product of the increase and decrease percentages. The decrease will generally result in a smaller area than the original.

Answer 1

The Correct Option is A

Let the side of the square be \( s \). The area of the square is: \[ \text{Area of square} = s^2 \] After increasing one side by 20% and decreasing the other side by 20%, the new dimensions of the rectangle are: \[ \text{New side 1} = s \times 1.2 \quad \text{and} \quad \text{New side 2} = s \times 0.8 \] Thus, the area of the rectangle is: \[ \text{Area of rectangle} = s \times 1.2 \times s \times 0.8 = s^2 \times 0.96 \] Therefore, the area of the rectangle is \( 96% \) of the area of the square.
Thus, the correct answer is \( 96% \).