1996 AHSME Problems/Problem 17
Problem
In rectangle , angle is trisected by and , where is on , is on , and . Which of the following is closest to the area of the rectangle ?
Solution
Since , each of the three smaller angles is , and and are both triangles.
Defining the variables as illustrated above, we have from
Then , and .
The area of the rectangle is thus .
Using the approximation , we get an area of just under , which is closest to answer . (The actual area is actually greater, since ).
Solution 1.1 (Better)
Use the process above, but use . You should get , which then you select . Notice that the actual area, when plugged into a calculator, yields about .
~hastapasta
See also
1996 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 16 |
Followed by Problem 18 | |
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