One side of the rectangle is 6 cm smaller than the other. The area of the rectangle is 55cm²

One side of the rectangle is 6 cm smaller than the other. The area of the rectangle is 55cm², find the lengths of its sides.

It is known from the condition that one of the sides of the rectangle is 6 cm smaller than the other. And the area of the rectangle is also known; it is 55 cm2.

In order to find the lengths of the sides of the rectangle, we introduce a variable and compose and solve the equation.

So, we denote by the variable x one of the sides of the rectangle, then the second side can be written as (x + 6).

S = a * b;

x (x + 6) = 55;

x2 + 6x – 55 = 0;

D = b ^ 2 – 4ac = 6 ^ 2 – 4 * 1 * (-55) = 36 + 220 = 256;

x1 = (-b + √D) / 2a = (-6 + 16) / 2 = 10/2 = 5;

x2 = (-b – √D) / 2a = (-6 – 16) / 2 = -22/2 = -11;

So, the length of one of the sides is 5 cm, and the second is 5 + 6 = 11 cm.