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An equilateral triangle of side length 2 is inscribed in a circle.  A rectangle, with side lengths x and y, is inscribed in another circle of the same size as the first one.  If the area of the rectangle is the same as that of the triangle, what are the sizes of x and y?

 Dec 27, 2021
 #1
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https://web2.0calc.com/questions/a-puzzle-for-those-who-are-bored

This was posted almost 7 years ago...

 Dec 28, 2021
 #2
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Equilateral triangle area       A = √3

Circle radius       r = 2/3(√3)

Circle diameter   z = 2r

Height       h = A / z

 

(w2 + h2)+(h2 + (z-w)2) = z2

 

x = sqrt(w2 + h2)

 

y = sqrt(h2 + (z-w)2)  smiley

 

 Dec 28, 2021

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