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Three squares are place side by side to form a rectangle. If the ratio of the length of the diagonal of the square to the length of the diagonal of a rectangle can be expressed in the form a/(√b) , where a and b are integers and a is square free, find a+b.

 Dec 16, 2019
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Let the side of a square  =  S

Then the diagonal of a square  =√2 *S

 

The diagonal of the rectangle  =  √ [ S^2  + (3S)^2  ]  =   √(10S^2)  =  √10*S

 

So....the ratio we want is

 

√2/ √10  =    √ (2/10)  = √ (1/5)  = √1 / √5  =   1  / √5

 

So

 

a + b   = 1  + 5    = 6

 

cool cool cool

 Dec 16, 2019

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