Me ):

an antique persian carpet has an area of (x2 + x - 20) ft2 and a length of (x + 5) ft. the rug is displayed on a wall in a museum. the wall has a width of (x+2) feet and an area of (x2+ 17 x + 30) ft2. write expressions for the length and width of both the rug and wall. then find the dimensions of the rug and the wall if x = 20 feet.

match the correct dimensions.

For the carpet:

Given:

Area = x^2 + x - 20 ft^2
Length = x+ 5 ft

As a carpet is rectangular, the area is defined as the product of the length and the width. To obtain an expression of the carpet's width, the area is to be divided by the length, which is shown below:

         __x_-_4___x + 5|x^2 + x - 20         x^2 + 5x                   -4x - 20          -4x - 20                               0

Therefore, the expression of width = x - 4.

Applying the value of x = 20 to obtain the measurements of the carpet, we obtain the following:

Width = x - 4 = 20 - 4 = 16ft
Length = x+ 5 = 20 + 5 = 25ft.

Therefore, the carpet is 25ft x 16ft.

For the wall:

The same principles apply to the wall as it is also assumed to be rectangular.

Given:
Area = x^2 + 17x + 30 ft^2
Width = x + 2

To obtain the expression for the wall's length, Area is to be divided by the Width, which is shown below:

         __x_+_15x + 2|x^2 + 17x + 30         x^2 + 2x                            15x + 30                  15x + 30                                                0

Therefore, the expression for the wall's length is x + 15.

Applying the value of x = 20 to obtain the wall's dimensions:

Length = x + 15 = 20 + 15 = 35ft.
Width = x + 2 = 20 + 2 = 22ft.

Therefore the wall has measurements of 35ft x 22ft.