The side of the square was increased by 30%. By what percentage has its area increased?

1) Let x be the length of the side of the square before magnification.

2) Then x ^ 2 is the area of the square before increasing its side.

3) Calculate 30% of the length of the side of the square:

x: 100 * 30 = 0.3x.

4) Then (x + 0.3x) = 1.3x – the length of the side of the square after the increase.

5) (1,3x) ^ 2 = 1,69x ^ 2 – the area of the enlarged square.

6) Let’s take the area of the square before the increase as 100%.

7) Let us denote by y% the area of the square after enlarging the side and make a note:

x ^ 2 – 100%;

1.69x ^ 2 – y%.

8) Let’s make the proportion:

x ^ 2: 1.69x ^ 2 = 100: y.

Hence y = 169.

8) By what percentage has the area of the square increased?

169 – 100 = 69%.

Answer: 69%.