Answer:
Length of rug in original design is 36 inches .
Width of rug in original design is  60 inches .
The problem says that the new design has length 3x inches longer  and x inches wider than the rug in the original plans .
New length of rug would be 3x inches longer than the original design  which is 36 inches .
Thus new length of rug is  ( 3x + 36  )  inches .
 New width of rug is x inches wider than the rug in the original plans which is 60 inches in original plan .
Thus new width of rug is   ( x + 60   )   inches .
Area of rectangle is  Length * Width  
Area of new rug is   ( 3x + 36 ) * ( x + 60 ) 
We distribute the terms using FOIL method .
( 3x + 36 ) *( x + 60 )  = 3x ( x + 60 ) + 36 ( x + 60 )
                                     =  3x² +  3x * 60  + 36 x  + 36 * 60 
                                     =   3x²  + 180 x + 36 x + 2160
     Combining like terms ,  3x² + 216 x + 2160
Thus the area of the rug with the new dimensions is 
( 3x + 36) ( x + 60 )  = 3x² + 216 x + 2160 .