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?

3x^2+216x+2160

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.