If the side of the square is reduced by 3 cm, then its area will decrease by 39 cm2. Find the area of the square.

Let us denote by a the length of the side of this square, expressed in centimeters.

Since the area of ​​any square is equal to the length of the side of this square in the second degree, the area S of this square is a ^ 2 cm ^ 2.

After? how the side of this square was reduced by 3 cm, the length of the side of the resulting square was a – 3 cm, and its area was (a – 3) ^ 2 cm ^ 2.

Since the area has decreased by 39 cm ^ 2, we can make the following equation:

a ^ 2 = (a – 3) ^ 2 + 39,

solving which, we get:

a ^ 2 = a ^ 2 – 6a + 9 + 39;

a ^ 2 = a ^ 2 – 6a + 48;

a ^ 2 – a ^ 2 + 6a = 48;

6a = 48;

a = 48/6 = 8 cm;

S = a ^ 2 = 8 ^ 2 = 64 cm ^ 2.

Answer: 64 cm ^ 2.