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Let $G$ be the center of equilateral triangle $XYZ.$  A dilation centered at $G$ with scale factor $-\frac{1}{5}$ is applied to triangle $XYZ,$ to obtain triangle $X'Y'Z'.$  Let $A$ be the area of the region that is contained in both triangles $XYZ$ and $X'Y'Z'.$  Find $\frac{A}{[XYZ]}.$

 Dec 28, 2023
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A  will have an area of (-1/5)^2   =1/25  of XYZ

 

So         (1/25) [ XYZ ] / [ XYZ ] =  1/25

 

cool cool cool

 Dec 28, 2023

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