The length of the rectangle was reduced by 3 cm, and the width was increased by 4 cm, resulting in a square

The length of the rectangle was reduced by 3 cm, and the width was increased by 4 cm, resulting in a square. Find the side of the square if the area of the rectangle is 30 cm2.

1. Let the side of the square be x cm;
2. Then the length of the rectangle is:
(x + 3) cm;
3. Width of the rectangle:
(x – 4) cm;
4. Knowing the area of the rectangle, compose and solve the equation:
(x + 3) * (x – 4) = 30;
x ^ 2 – 4x + 3x – 12 – 30 = 0;
x ^ 2 – x – 42 = 0;
D = b ^ 2 – 4 * a * c = 1 + 168 = 169 = 132;
x1 = (-b + √D) / (2 * a) = (1 + 13) / 2 = 7;
x2 = (-b – √D) / (2 * a) = (1 – 13) / 2 = -6 – not a solution;
That is, the side of the square is 7 cm;
Answer: the side of the square is 7 cm.