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A large square is divided into 4 small congruent rectangles and a small square as shown. The areas of the large and small squares are 25 and 7, respectively. What is the length of a diagonal of a small rectangle?

 

 Dec 31, 2019
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The side of the large square  =   sqrt (25)  =  5

The side of the small square =  sqrt (7)

 

The smaller  dimension of a rectangle, d, can be found as

 

2d  + sqrt (7)  = 5

2d =  5 - sqrt (7)

d  =  [ 5 - sqrt (7) ]  / 2  =    (5/2) - sqrt (7) / 2

 

So  the larger dimension, D  =  5 - [ 5/2 - sqrt(7) / 2 ]  =  5/2 + sqrt (7)  / 2

 

So.....the  length of the diagonal  of a rectangle  = 

 

sqrt [ d^2 + D^2 ]  = 

 

sqrt  [ ( 5/2 - sqrt(7) / 2 )^2   + ( 5/2 + sqrt (7)/2)^2 ]  =

 

sqrt [ 25/4  + 7/4  + 25/4  + 7/4]  =

 

sqrt [ 64/4]  =

 

sqrt [ 16]  =

 

4

 

 

cool cool cool

 Dec 31, 2019

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