1997 PMWC Problems/Problem T1
Problem
Let be an equilateral triangle with sides of length three units. , , , , , and divide the sides into lengths of one unit. Find the ratio of the area of the shaded quadrilateral to the area of the triangle .
Solution
Triangles UWQ, PUY, UWX, and UXY are all right triangles with side lengths 1, , and 2. Thus and .
See Also
1997 PMWC (Problems) | ||
Preceded by Problem I15 |
Followed by Problem T2 | |
I: 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 T: 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 |