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

 

 Apr 23, 2024
 #1
avatar+14943 
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Find the area of the strip.

 

Let a be the distance of the base 10 touched by the strip.

Let alpha be the slope angle of the strip.

 

\(tan(\alpha)=\frac{8}{10-a}\\ sin(\alpha )=\frac{1}{a}\\ \alpha =atan(\frac{8}{10-a})=asin(\frac{1}{a})\\ atan(\frac{8}{10-a})-asin(\frac{1}{a})=0\)

 

\(\color{green}WolframAlpha\\ \color{green}a=\frac{8\sqrt{163}}{63}-\frac{10}{63}\\\)

\(\color{blue}a=1.4625\\ A=8\cdot 1.4625\\ \color{blue}A=11.7\)

 

\(\color{blue}The\ area\ of\ the\ strip\ is\ 11.7\ .\)

 Apr 25, 2024

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