Question

You have a square that has a side length of $1$ centimeter. Each minute, $2$ centimeters are added to the side length. After $10$ minutes, what will be the difference between the area of the last square and the area of the initial square in square centimeters (do not include the units in your answer)?

Answer 1

Difference in area of the last square and the initial square = 440 cm²

Explanation:

Length of the side of a square = 1 cm

Area of the square = (side)² = 1 cm²

Addition of side length every minute = 2 cm

After x minutes length of each side of the square = (1 + 2x) cm

If x = 10 minutes

Length of each side of the square = [1 + 2(10)]

= 21 cm

Area of the square after 10 minutes = (21)²

= 441 cm²

Therefore, difference in area of the last square and area of the initial square

= 441 - 1

= 440 cm²