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A square has a side length of 10 inches. Congruent isosceles right triangles are cut off each corner so that the resulting octagon has equal side lengths. How many inches are in the length of one side of the octagon? Express your answer as a decimal to the nearest hundredth.

 

 Dec 1, 2018
 #1
avatar+98196 
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Let the side length of the octagon = S.....this = the hypotenuse of an isosceles triangle

So...the length of one of the legs of the isosceles triangles =   S/√2

 

And the side of the square = 

 

S + 2S/√2 =  S + S√2

 

So

 

S + S√2  = 10

S(1 + √2)  = 10    divide bot sides by ( 1 + √2)

 

S =     10   / ( 1 + √2 )   ≈    4.14  (inches)

 

 

cool cool cool

 Dec 1, 2018

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