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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?

 Jan 27, 2019
 #1
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The length of the side of the large square = 5  units

The length of the side of the small square = √7   units

 

The length of the shorter side of a rectangle =   [ 5 - √7] / 2

 

The length of the longer side of the rectangle =  5 - [ 5 - √7 ] / 2   =  [ 5 +  √7]/ 2

 

So.....the squared length of the rectangle's diagonal  =

 

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

 

[ 25 - 10√7 + 7 ] / 4   +  [ 25 + 10√7 + 7 ] / 4  =

 

[ 64 / 4 ]   =

 

16

 

So......the diagonal length =  √16  =   4 units

 

 

cool cool cool

 Jan 27, 2019

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