Find the area of a rectangle if its width is 10 cm less than its length and the half-perimeter is 26 cm.

1. Let’s denote the length of the rectangle by A cm, and the width by B cm.

2. Then from the first condition of the problem we will compose the first equation: A – B = 10.

3. The semi-perimeter of a rectangle is equal to the sum of its length and its width. That is, in accordance with the second condition of the problem, we will compose the second equation: A + B = 26.

4. Add the first and second equations. We get: 2 * A = 36. Hence A = 18 cm.

5. From the first equation of the problem B = A – 10 = 18 – 10 = 8 cm.

6. The area of the rectangle S is equal to the product of its length by its width:
S = A * B = 18 * 8 = 144 cm2.

Answer: the area of the rectangle is 144 cm2.