2019 Mock AMC 10B Problems/Problem 15

Revision as of 23:23, 13 December 2019 by Awesome 360 (talk | contribs) (Created page with "The area of the larger square is 144, so each side length is 12. m + n = 12. Also, Each of the smaller 4 triangles are right triangles, so m²+n²= 108. n=12-m m²+(12-m)²...")
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The area of the larger square is 144, so each side length is 12. m + n = 12. Also, Each of the smaller 4 triangles are right triangles, so m²+n²= 108.

n=12-m m²+(12-m)²=108 m²+144-24m+m²=108.

Solving for m gives m= 12+sqrt(72)/2, m = 6+3sqrt2, a=6, b=3, c=2. a+b+c=11. (A)

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