Difference between revisions of "1996 AHSME Problems/Problem 17"
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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{\text{E}}</math>. (The actual area is actually greater, since <math>\sqrt{3} > 1.7</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{\text{E}}</math>. (The actual area is actually greater, since <math>\sqrt{3} > 1.7</math>). | ||
+ | |||
+ | == Solution 1.1 (Better) == | ||
+ | Use the process above, but use <math>\sqrt{3} \approx 1.73</math>. You should get <math>[ABCD]=150.84</math>, which then you select <math>\boxed{\text{E}}</math>. Notice that the actual area, when plugged into a calculator, yields about <math>151.0614872</math>. | ||
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+ | ~hastapasta | ||
==See also== | ==See also== |
Latest revision as of 15:24, 12 May 2022
Contents
[hide]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 | |
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 |
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