Let Original rectangle has length L and Width W.
Perimeter = 18 inches
→2(L+W)=18
Dividing both sides by 2,we get
L+W=9 ........(1)
Now, new rectangle is formed by doubling the width Wand tripling the length L.
New length=3 L
New Breadth=2W
New perimeter=46 inches
→2(3 L+2W)=46
Dividing both sides by 2, we get
3L+ 2W=23
→L=9-W [Using 1]
Substituting in (2), we get
3(9-W)+2W=23
27-3W+W=23
W=27-23
W=4
and L=9-4=5 inches
So, Original rectangle has Length=5 inches, and Width=4 inches