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A right triangle is inscribed in a circle with a diameter 100 units long. What is the maximum perimeter of the triangle?

 May 6, 2021
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The hypotenuse  will  lie on the  diameter

 

The  perimeter is  maximized when the legs  are equal....using  the Pythagorean Theorem

 

L^2  +  L^2  = 100^2

 

2L^2  =100^2

 

L^2  =  100^2/2

 

L  =   100/sqrt 2

 

So...the  max perimeter is     100 +  2 * 100/sqrt 2  =    100 ( 1 + sqrt 2) units  ≈  241.42  units

 

cool cool cool

 May 6, 2021

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