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avatar+1055 

The rectangle with the area of 12 cm2 has a specific ratio  a : b. When folded in half along the longer sides, a new, smaller rectangle, has the same ratio as the original one. Find the sides  a and b, and the sides of a new rectangle  a1 and  b1

 Dec 25, 2019
edited by Dragan  Dec 25, 2019
edited by Dragan  Dec 25, 2019
edited by Dragan  Dec 25, 2019
 #1
avatar+111435 
+2

Let   a be the longer side of the  original rectangle and  b be  the shorter side

So

 a*b  =12

b  =  12/a   (1)

 

When folded in half, the  longer side  =  b   and the shorter side  is  a/2

 

a/ b  =  b / (a/2)

 

a/b  = 2b / a

 

a^2  = 2b^2

 

a = √2b

 

So

 

a * b   = 12

 

√2 b* b  = 12

 

b^2  =  12/√2

 

b^2 =  6√2

 

b^2 = √72

 

b = 4√72    

 

And a  = √2 4√72  

 

So

 

a / b =  √2 4√72  / [  4√72  ] =  √2

 

And   b/ [a/2]  =   2b / a  =  2  4√72  / [√2 4√72 ] =  2/√2  = √2

 

So

 

a  = √2 4√72 

     

b =  4√72 

 

And

 

a1  = b =   4√72 

 

b1  =  a/2  =   [√2 4√72] / 2

 

cool cool cool

 Dec 25, 2019

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