Difference between revisions of "1996 AHSME Problems/Problem 17"
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The area of the square is thus <math>xy = 6\sqrt{3}(18 - 2\sqrt{3}) = 108\sqrt{3} - 36</math>. | The area of the square is thus <math>xy = 6\sqrt{3}(18 - 2\sqrt{3}) = 108\sqrt{3} - 36</math>. | ||
− | Using the approximation <math>\sqrt{3} \approx 1.7</math>, we get an area of just under <math>147.6</math>, which is closest to answer <math>\boxed{ | + | Using the approximation <math>\sqrt{3} \approx 1.7</math>, we get an area of just under <math>147.6</math>, which is closest to answer <math>\boxed{E}</math>. (The actual area is actually greater, since <math>\sqrt{3} > 1.7</math>). |
==See also== | ==See also== | ||
{{AHSME box|year=1996|num-b=16|num-a=18}} | {{AHSME box|year=1996|num-b=16|num-a=18}} |
Revision as of 15:29, 19 August 2011
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 square is thus .
Using the approximation , we get an area of just under , which is closest to answer . (The actual area is actually greater, since ).
See also
1996 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 16 |
Followed by Problem 18 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 | ||
All AHSME Problems and Solutions |