Cynthia besch wants to buy a rug for a room that is 1919 ft wide and 2727 ft long. she wants to leave a uniform strip of floor around the rug. she can afford to buy 153153 square feet of carpeting. what dimensions should the rug have?

The dimension of the rug would be 17 ft × 9 ft.

Step-by-step explanation:

Given

length of the room = 27 ft.

width of the room = 19 ft.

suppose, she leaves a uniform strip of x ft. around the rug.

So,

The length of rug = (27-2x)ft.

Width of rug= (19-2x)ft.

∴ Area of the rug= length×width

According to the question,

       ( subtract 153 both sides)

           ( Middle term splitting)

or             ( zero product property)

or

if x=18, dimension would be negative  ( Not possible)

Thus, x= 5

Hence,

length of rug= 27-10=17 ft.

width of rug= 19-10=9 ft.