1984 AHSME Problems/Problem 8
Problem
Figure is a trapezoid with , , , , and . The length of is
Solution
Drop perpendiculars from and to , thus forming a 30-60-90 right triangle, a 45-45-90 right triangle, and a rectangle, as shown in the diagram. Since is a rectangle, we have . Also, from the properties of 45-45-90 right triangles, we have . Again since is a rectangle, , too. From the properties of 30-60-90 right triangles, we have . Therefore, .
See Also
1984 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 7 |
Followed by Problem 9 | |
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