The area of the rectangle is 28, find its larger side if it is 12 larger than the smaller side.

1. Let’s denote the length of the shorter side of the rectangle through x.

2. Determine the length of the larger side of the rectangle:

(x + 12).

3. Let’s compose and solve the equation:

(x + 12) * x = 28;

x2 + 12x = 28;

x2 + 12x – 28 = 0;

D = 122 – 4 * 1 * (-28) = 144 + 112 = 256

x1 = (-12 + √256) / (2 * 1) = (-12 + 16) / 2 = 4/2 = 2;

x2 = (-12 – √256) / (2 * 1) = (-12 – 16) / 2 = -28/2 = -14.

-14 – does not meet the condition of the problem.

4. The length of the shorter side of the rectangle is 2.

5. What is the length of the longer side of the rectangle?

2 + 12 = 14.

Answer: The length of the longer side of the rectangle is 14.