Difference between revisions of "2024 AMC 8 Problems/Problem 11"
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+ | ==Video Solution (easy to digest) by Power Solve== | ||
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==Video Solution by Math-X (First understand the problem!!!)== | ==Video Solution by Math-X (First understand the problem!!!)== | ||
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~Math-X | ~Math-X | ||
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==Video Solution 3 by SpreadTheMathLove== | ==Video Solution 3 by SpreadTheMathLove== | ||
https://www.youtube.com/watch?v=RRTxlduaDs8 | https://www.youtube.com/watch?v=RRTxlduaDs8 |
Revision as of 18:53, 26 January 2024
Contents
Problem
The coordinates of are , , and , with . The area of is 12. What is the value of ?
Solution 1
The triangle has base which means its height satisfies This means that so the answer is
Solution 2
Label point as the point at which . We now have , where the brackets denote areas. On the righthand side, both of these triangles are right, so we can just compute the two sides of each triangle. The two side lengths of are and . The two side lengths of are and Now,
Dividing by gives so
-Benedict T (countmath1)
Video Solution (easy to digest) by Power Solve
https://www.youtube.com/watch?v=2UIVXOB4f0o
Video Solution by Math-X (First understand the problem!!!)
~Math-X