One side of the rectangle is 2 cm smaller than the other. Find the larger side of the rectangle if its area is 143.

Let’s denote the large side of the rectangle with the letter x, then the second side will be equal to (x – 2). The area of the rectangle is equal to the product of its sides, since the area is 143, we will compose the equation:

x (x – 2) = 143.

x² – 2x – 143 = 0.

We solve the quadratic equation using the discriminant:

a = 1; b = -2; c = -143;

D = b² – 4ac; D = (-2) ² – 4 * 1 * (-143) = 4 + 572 = 576 (√D = 24);

x = (-b ± √D) / 2a;

x1 = (2 – 24) / 2 = -22/2 = -11 (not suitable).

x2 = (2 + 24) / 2 = 26/2 = 13.

Answer: The large side of the rectangle is 13.