The rectangle was divided into parts, the area of which is 2: 9. Find its area if one part is 42 cm2 larger than the other.

Let us determine by how many equal parts by area one figure obtained from a rectangle surpasses another, when, according to the condition of the task, we know that these two figures are related by their areas as 2 to 9:
9 – 2 = 7.
Let us determine what the area of one such equal part will equal when it is known that the area of one figure is 42 cm2 larger than the other:
42: 7 = 6.
Determine how many such equal parts are in the rectangle:
2 + 9 = 11.
Let’s find out its area:
11 * 6 = 66.
Answer: 66 cm2.