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 .