Question

Cynthia Besch wants to buy a rug for a room that is 20 ft wide and 26 ft long. She wants to leave a uniform strip of floor around the rug. She can afford to buy 160 square feet of carpeting. What dimensions should the rug​ have?

Answer 1

10 ft by 16 ft

Explanation:

Let the length of the strip be x

So from both edges the length covered by the rug will be:

(20-2x) and (26-2x)

The area of this will be;

(20-2x)(26-2x) = 160

520-40x-52x + 4x^2 = 160

4x^2-92x+520-160 = 0

4x^2 -92x + 360 = 0

x^2 -23x + 90 = 0

x^2 - 18x -5x + 90 = 0

x(x-18)-5(x-18) = 0

(x-5)(x-18) = 0

x = 5 or 18

if x is 5; dimensions are;

(20-10) by (26-10)

= 10 by 16

if x = 18; dimensions will

not be possible as it will

lead to negative numbers

So the dimensions of the rug will be 10 ft by 16 ft