4. Variant 1.

A rectangle was cut into three rectangles, two of which have dimensions 9 m $\times$ 12 m and 10 m $\times$ 15 m. What is the maximum area the original rectangle could have had? Express your answer in square meters.
Answer: 330

Solution. Since the sizes of the two rectangles are fixed, in order for the original rectangle to have the maximum area, the third rectangle must have the largest area. Since the two given rectangles do not have the same sides, the largest area will be obtained by attaching the smaller side of one rectangle to the larger side of the other. This results in a rectangle of size $12 \times(9+15)$ or a rectangle of size $15 \times(10+12)$. The area of the first is 288, and the second is 330, so the answer is 330.

Variant 2.

A rectangle was cut into three rectangles, two of which have dimensions 8 m $\times 12$ m and 10 m $\times 14$ m. What is the maximum area the original rectangle could have had? Express your answer in square meters.

Answer: 308