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

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

1. Let the smaller side of the rectangle be x cm, then the larger side is (x + 2) cm.

2. Find the area of the rectangle by multiplying its sides by each other

x * (x + 2) = x ^ 2 + 2x cm2, and by the condition of the problem 120 cm2.

3. Let’s compose and solve the equation.

x ^ 2 + 2x = 120;

x ^ 2 + 2x – 120 = 0;

D = 2 ^ 2 – 4 * (-120) = 4 + 480 = 484, D> 0.

x1 = (- 2 + √484) / 2 = (-2 + 22) / 2 = 10;

x2 = (-2 – √484) / 2 = – 24/2 = – 12 does not fit the problem.

10 cm is the smaller side of the rectangle, then the larger side is 10 + 2 = 12 cm.

Answer: 10 cm; 12 cm.