One side of the rectangle is 4 cm smaller than the side of the square, and the other side is 1 cm

One side of the rectangle is 4 cm smaller than the side of the square, and the other side is 1 cm larger than the side of the square. Find the area of the square if it is 19cm2 larger than the area of the rectangle.

1. Let the side of the square be x, then one side of the rectangle is (x – 4) and the other is (x + 1).
2. The area of the rectangle S1 is equal to:
S1 = (x – 4) * (x + 1);
3. The area of the square S2 is:
S2 = x * x = x ^ 2;
4. It is known that the area of a square is 19 cm ^ 2 larger than the area of a rectangle. We get the equation:
S2 = S1 + 19;
x ^ 2 = (x -4) * (x + 1) + 19;
x ^ 2 = x ^ 2 + x – 4 * x – 4 + 19;
x ^ 2 – x ^ 2 – x + 4 * x = 19 – 4;
3 * x = 15;
x = 15/3 = 5;
5. Find the area of the square:
S2 = x ^ 2 = 5 ^ 2 = 25;
6. Answer: the area of the square is 25 cm ^ 2.