# 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.

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