# One side of the rectangle is 2 cm larger than the other side. Find the sides of a rectangle

**One side of the rectangle is 2 cm larger than the other side. Find the sides of a rectangle if its area is 120 cm ^ 2. Through a system of equations.**

Let the length of one side be x cm and the length of the other side y cm.

Area S = 120 cm ^ 2.

We compose the first equation of the system, taking into account that the length of the first is 2 cm larger than the second:

x-y = 2;

We compose the second equation using the formula for the area of a rectangle:

xy = 120;

We have a system of equations:

x-y = 2;

xy = 120;

To find a solution to the system of equations, we use the substitution method, we express one variable in the first equation through the second, we have:

x = y + 2;

xy = 120;

Substituting the expression for x the second equation, we have:

(y + 2) y = 120;

y ^ 2 + 2y-120 = 0;

By Vieta’s theorem, we have:

y1 = 10;

y2 = -12 – the length cannot be negative, we do not use this root;

y = 10 (cm);

x = 10 + 2 = 12 (cm).

Answer: 12 cm, 10 cm.