Question

Jessica made plans to weave a rectangular jute rug, but she needs to update the plans to change the dimensions of the rug. The original design has a length of 36 inches and a width of 60 inches. The rug from the new plans will be 3x inches longer and x inches wider than the rug in the original plans. Which of the following functions will give the area of the rug with the new dimensions, in square inches?

Answer 1

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 .

Answer 2

Answer:

3x^2+216x+2160

Step-by-step explanation: