2006 Cyprus MO/Lyceum/Problem 14
Problem
The rectangle is a small garden divided to the rectangle and to the square , so that and the shaded area of the triangle is . The area of the whole garden is
Solution
The area of triangle is equal to the area of triangle , so the area of rectangle is . Let and . , and . Thus
. Thus and . So we have .
Note: The answer theoretically can be 12, since we are not given that . If and , we have a 2*2 square and a 4*2 rectangle, with a diagonal of . But 12 is not one of the answers included.
See also
2006 Cyprus MO, Lyceum (Problems) | ||
Preceded by Problem 13 |
Followed by Problem 15 | |
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