Let the width of the rectangle be x units, so that length will be 2x+2 units

 

The diagonal would be √ [ x2 + (2x+2)2  ]  units and  the length of the rectangle will also be equal to √ [ x2 + (2x+2)2  ] – 1 .

 

Thus √ [ x2 + (2x+2)2  ] – 1 = 2x +2. 

 

 Or, √ [ x2 + (2x+2)2  ] = 2x +3.  Now square both sides

 

 x2 + (2x+2)2   = (2x+3)2 .  Simplifying the equation it would be

 

5x2 + 8x +4 = 4x2 + 12x +9

 

x2 -4x -5=0 ,

 

0r (x-5)(x+1)=0. which gives x= 5 or x= -1.  Reject the negative value of x. this x=5, which is the width of the triangle

 

Hence its length will be 2(5)+2 = 12 cms

 

Perimeter will be 2[ x +2x+2]

                        

                          = 6x + 4

 

                          =  34 cms      Answer