One of the sides of the rectangle is 1.5 cm larger than the other, and its area is 10 cm2.

One of the sides of the rectangle is 1.5 cm larger than the other, and its area is 10 cm2. Find the sides of this rectangle.

Let one side of the rectangle be x cm, then the second side of the rectangle is equal to (x + 1.5) cm.By the condition of the problem, it is known that the area of the rectangle is equal to the product of its sides, i.e. x (x + 1.5) cm ^ 2 or 10 cm ^ 2. Let’s make an equation and solve it.

x (x + 1.5) = 10.

x ^ 2 + 1.5x = 10;

x ^ 2 + 1.5x – 10 = 0;

D = b ^ 2 – 4ac;

D = 1.5 ^ 2 – 4 * 2 * (-10) = 2.25 + 40 = 42.25; √D = 6.5;

x = (-b ± √D) / (2a);

x1 = (-1.5 + 6.5) / (2 * 1) = 5/2 = 2.5 (cm) – one side;

x2 = (-1.5 – 6.5) / 2 = -8/2 = -4 – side length cannot be negative.

x + 1.5 = 2.5 + 1.5 = 4 (cm) – the second side.

Answer. 2.5 cm; 4 cm.