The side of the square was increased by 4 cm and got a square, the area of which is 196 cm squared.

The side of the square was increased by 4 cm and got a square, the area of which is 196 cm squared. Find the area of the starting square.

We know that the side of the square was increased by four cm, then we denote the initial length of the side of the square as x, then we can write that the side of the new square is (x + 4) cm, we write the area of the square:
(x + 4) ^ 2 = 196;
Let’s open the square:
x ^ 2 + 8x + 16 = 196;
x ^ 2 + 8x – 180 = 0;
Let’s find the discriminant:
D = 64 – (4 * (-180)) = 64 + 720 = 784;
The root of the discriminant is 28, then x is:
x1 = (-8 + 28) / 2 = 10 cm;
x2 = (-8 – 28) / 2 = -18 cm – not suitable.
Starting square area:
10 ^ 2 = 100 cm2.
Answer: 100 cm2.