Problem:
A square with area is inscribed in a square with area , with one vertex of the smaller square on each side of the larger square. A vertex of the smaller square divides a side of the larger square into two segments, one of length and the other of length . What is the value of
Answer Choices:
A.
B.
C.
D.
E.
Solution:
The area of the region inside the larger square and outside the smaller square has total area and is equal to the area of four congruent right triangles, each with one side of length and the other of length . The area of each triangle is . If , then .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions