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A rectangle contains a strip of width $1,$ as shown below.  Find the area of the strip.

 Jun 1, 2024
 #1
avatar+806 
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Let x be the length from the right edge to the strip. 

We have

\([rectangle]=1\cdot\sqrt{8^2+x^2}+8x=10\cdot 8\\ \sqrt{8^2+x^2}=80-8x\\ 8^2+x^2=6400-1280x+64x^2\\ 63x^2-1280x+6336=0\)

\(x = {-b \pm \sqrt{b^2-4ac} \over 2a}=\frac{640-8\sqrt{163}}{63}\\ x=8.5375\\ [strip]=1\cdot \sqrt{8.5375^2+8^2}\\ [strip]=11.7\)

 

Thanks! :)

 Jun 2, 2024

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