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A large square is divided into  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 17, 2020
 #1
avatar+111437 
+1

The side of the large square   = 5

The side of the small square  =  √7

 

Let the smaller dimension of a ectangle  = x

Let the larger dimension of a rectangle  = y

 

And we have this  system

    

2x + √7  = 5    ⇒    x  =  ( 5 - √7) / 2       (1)

 

x + y  = 5    (2)

 

Sub (1)  into (2)

 

(5 - √7) / 2  +  y  = 5

 

y  =  5 - (5 - √7)/2  = 5/2 + √7/2  =  ( 5 + √2)/ 2

 

The  square of the diagonal  length  =

 

x^2  + y^2  =

 

(5 - √7)^2 / 4  +  ( 5 + √7)^2/4  =

 

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

 

[ 50  + 14 ]  / 4  =

 

64/ 4  =

 

16

 

So....the length of the diagonal of a rectangle =  √16   =   4

 

 

cool cool cool

 Jan 17, 2020
 #2
avatar+1072 
+1

Rectangle diagonal:          D = sqrt [ (√25 - √7)/2 ]2 + [√25 - (√25 - √7)/2 ]2     indecision      

 Jan 17, 2020

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