How many times will the area of a square increase if its side is increased 3 times?

1. Let us denote the side of the square by the variable a.

2. Find the area of a square with side a.

S1 = a ^ 2.

3. Find the side of the square, enlarged 3 times.

a × 3 = 3a.

4. Find the area of a square with a side enlarged 3 times.

S2 = (3a) ^ 2 = 3 ^ 2 × a ^ 2 = 9a ^ 2.

5. Let’s find how many times the area of the square will increase if its side is increased by 3 times.

S2 / S1 = (9a ^ 2) / (a ^ 2) = 9 times.

Answer: if the side of a square is enlarged 3 times, its area will increase 9 times.