The area of the rectangle is 675 cm2. Find the sides of the rectangle if one of them is 30 cm smaller than the other.

Let one side of the rectangle be equal to x cm, then the second side of the rectangle is equal to (x – 30) cm. By the problem statement, it is known that the area of a rectangle is equal to the product of its sides, i.e. x (x – 30) cm ^ 2 or 675 cm ^ 2. Let’s make an equation and solve it.

x (x – 30) = 675;

x ^ 2 – 30x = 675;

x ^ 2 – 30x – 675 = 0;

D = b ^ 2 – 4ac;

D = (-30) ^ 2 – 4 * 1 * (-675) = 900 + 2700 = 3600; √D = √3600 = 60;

x = (-b ± √D) / (2a);

x1 = (30 + 60) / 2 = 90/2 = 45 (cm) – the first side;

x2 = (30 – 60) / 3 = -30/2 = -15 – side length cannot be negative;

x – 30 = 45 – 30 = 15 (cm) – the second side.

Answer. 45 cm; 15 cm.