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