Question

Cynthia Besch wants to buy a rug for a room that is 18 ft wide and

26 ft long. She wants to leave a uniform strip of floor around the
rug. She can afford to buy 128 square feet of carpeting. What
dimensions should the rug have?

Answer 1

8 ft by 16 ft

Explanation:

Let the width of the strip be x.

Then, the dimensions of the rug are (26-2x) and (18-2x).

So,

`(26-2x)(18-2x)=128 \\ \\ 4(13-x)(9-x)=128 \\ \\ (13-x)(9-x)=32 \\ \\ x^2 -22x+117=32 \\ \\ x^2 -22x+85 =0 \\ \\ (x-5)(x-17)=0 \\ \\ x=5, x=17`

If x=17, then both dimensions are less than 0, so x must equal 5.

So, the dimensions are 8 ft by 16 ft.