Problem:
A square of area is inscribed in a square of area , creating four congruent triangles, as shown below. What is the ratio of the shorter leg to the longer leg in the shaded right triangle?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Let be the length of the shorter leg of the right triangle. Then the longer leg has length . The hypotenuse has length . By the Pythagorean Theorem,
This equation simplifies to , and the Quadratic Formula gives the solutions . The requested ratio is
The problems on this page are the property of the MAA's American Mathematics Competitions