One side of the rectangle is 2 larger than the other side. Find the sides of the rectangle if its area is 120cm2.

We denote one of the sides of the rectangle through X.

By the condition of the problem, the second sides of the rectangle are 2 cm more.

(X + 2) is the value of the second side of the rectangle.

Knowing that the area of ​​the rectangle is 120, we compose and solve the equation:

X * (X + 2) = 120.

Expand the brackets:

X ^ 2 + 2X = 120;

X ^ 2 + 2X – 120 = 0.

We solve the quadratic equation using the formula with the second even coefficient:

X1,2 = (-1) ± √1 + 120;

X1,2 = (-1) ± 11;

X1 = 10; X2 = (-12);

The value cannot be negative, therefore X2 is not taken into account.

Find the second side of the rectangle:

(X + 2) = 10 + 2 = 12.

Answer: the sides of the rectangle are 10 cm and 12 cm.