The area of the square is 63 cm² larger than the area of the rectangle. One side of the rectangle is 3cm

The area of the square is 63 cm² larger than the area of the rectangle. One side of the rectangle is 3cm larger and the other 6cm smaller than the side of the square. Find the area of the square.

1. One side of the square is x cm.
2. One of the sides of the rectangle is equal to (x + 3) cm.
3. The other side of the rectangle is (x – 6) cm.
4. Determine what is the area of the rectangle.
(x + 3) * (x – 6) = x ^ 2. – 6x + 3x – 18 = (x ^ 2. – 3x – 18) cm ^ 2.
5. Let’s calculate the area of the square.
x * x = x ^ 2.
6. Let’s compose and solve the equation.
x ^ 2. – 63 = x ^ 2. – 3x – 18;
x ^ 2. – x ^ 2. + 3x = 63 – 18;
3x = 45;
x = 45/3 = 15;
x = 15;
6. The side of the square is x = 15 cm.
7. Find out the area of the square.
15 * 15 = 225 cm ^ 2.
Answer: The area of the square is 225 ^ 2.