Question

Cynthia Besch wants to buy a rug for a room that is 20 ft wide and 31 ft long. She wants to leave a uniform strip of floor around the rug. She can afford to buy 350 square feet of carpeting. What dimensions should the rug​ have?

Answer 1

Answer:

The dimensions should the rug​ have: length = 25 feet and width of 14 feet.

Step-by-step explanation:

Dimension of the room is 20 ft wide and 31 ft long

Area of rug purchased by Cynthia Besch = $A=350 ft^2$

Suppose she leave strip of floor which is x ft thick.

Length of the rug= l = (31-x) ft

Width of the rug= w = (20-x) ft

Area of the rug,A = l × w

$350 ft^2= (31-x) ft \times (20-x) ft$

$350=620-51x+x^2$

$x^2-51x+270=0$

$x^2-45x-6x+270=0$

$x(x-45)-6(x-45)=0$

$(x-45)(x-6)=0$

x = 45 , 6

x = 6 (accept), x= 45 ,(reject, larger than length of the room )

Length of the rug= l = (31-x) ft = 31 - 6 ft = 25 ft

Width of the rug= w = (20-x) ft = 20 - 6 ft = 14 ft

Answer 2

20*31=620
620/2=310
20/2=10
31/2=15.5
The dimensions should be  10*15.5