What can be the lengths of the sides of a rectangle, the perimeter of the second is 26 cm, and the area is 40 cm2?

By the condition of the problem, we know the perimeter of the rectangle, equal to 26. If we divide this perimeter in half, then we will find the sum of the length and width of the rectangle:

26: 2 = 13 (cm).

Also, from the condition of the problem, we know the area of the rectangle, equal to 40 cm². Thus, the length and width of the rectangle should be equal to such values, the sum of which is 13 cm, and the product is 40 cm².

These numbers are the numbers 8 and 5:

P = 2 (8 + 5) = 26 (cm).

S = 5 * 8 = 40 (cm²).

Answer: the length is 8 cm, the width is 5 cm.