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

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

2. Let’s find its area.

S1 = a ^ 2.

3. Find the side of the square after doubling it.

a × 2 = 2a.

4. Find the area of a square with a side enlarged 2 times.

S2 = (2a) ^ 2 = 2 ^ 2 × a ^ 2 = 4a ^ 2.

5. Let’s find how many times the area of the square will increase after increasing its side by 2 times.

S2 / S1 = (4a ^ 2) / a ^ 2 = 4.

Answer: if you enlarge the side of a square by 2 times, its area will increase by 4 times.