If the side of the square is increased by 10%, then its area will increase by 5.25 dm2. Calculate the side of the square

If the side of the square is increased by 10%, then its area will increase by 5.25 dm2. Calculate the side of the square and its area before enlarging.

Area of a square (S) = a²
It is said that if a + 0.1a, then S becomes S + 5.25
Let’s compose a system of equations:
1.a² = S
2.1.21a² = S + 5.25
Substitute S instead of a² in the second equation:
1.21S = S + 5.25
1.21S-S = 5.25
0.21S = 5.25
S = 5.25 / 0.21
S = 25 dm²
From here find the modem:
a = √S, therefore a = 5 dm
Answer: a = 5 dm; S = 25 dm²