Problem:
Rectangles and , and squares , , and , shown below, combine to form a rectangle that is units wide and units high. What is the side length of in units?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
We represent the lengths of each square as respectively. The length of the rectangle is as these three squares span the entirety of a side of the large rectangle. Therefore, we have the equation:
Also, the height of the large rectangle is the sum of the height of and . Now, note that the sum of the height of and is , so the height of is equal to . Therefore, the height of the large rectangle is , which means:
Subtracting both of our results gives:
This implies:
Thus, the correct answer is .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions