A rectangle is divided into four smaller rectangles. The areas of three of these rectangles are 6, 15 and 25, as shown. The area of the shaded rectangle is
(A) 7
(D) 16
(B) 15
(E) 10
(C) 12
| 6 | 15 |
| :--- | :--- |
| | 25 |
Problem 581
Official solution
We can determine the area of the shaded region by guessing the side lengths of the various rectangles and then cross-checking our results. Let us suppose that the top left rectangle has a width of 2 and a height of 3 . Then the top right rectangle has a width of 5 , since its height is also 3. Thus, we can conclude that the height of the bottom right rectangle is 5. This tells us that the shaded rectangle is 2 by 5 , or has an area of 10 . This problem can also be solved with a more algebraic approach, but this is the most straightforward way.
ANSWER: (E)