2007 AMC 10B Problems/Problem 21
Problem
Right has and Square is inscribed in with and on on and on What is the side length of the square?
Solution 1
There are many similar triangles in the diagram, but we will only use If is the altitude from to and is the sidelength of the square, then is the altitude from to By similar triangles,
Find the length of the altitude of Since it is a right triangle, the area of is
The area can also be expressed as so
Substitute back into
Solution 2
Let be the side length of the inscribed square. Note that .
Then we can setup the following ratios:
But then
Video Solution by OmegaLearn
https://youtu.be/FDgcLW4frg8?t=4662
~ pi_is_3.14
See Also
2007 AMC 10B (Problems • Answer Key • Resources) | ||
Preceded by Problem 20 |
Followed by Problem 22 | |
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