SOLUTION: A rug is to fit in a room so that a border of consistent width is left on all four sides. If the room is 9 feet by 25 feet and the area of the rug is 57 square feet, how wide will

Algebra ->  Test -> SOLUTION: A rug is to fit in a room so that a border of consistent width is left on all four sides. If the room is 9 feet by 25 feet and the area of the rug is 57 square feet, how wide will      Log On


   

Question 622425: A rug is to fit in a room so that a border of consistent width is left on all four sides. If the room is 9 feet by 25 feet and the area of the rug is 57 square feet, how wide will the border be?
Answers I can choose from:
3ft
4ft
5ft
5.5ft
Thank you!
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi,

A rug is to fit in a room so that a border of consistent width is left on all four sides.  

If the room is 9 feet by 25 feet and the area of the rug is 57 square feet,

how wide highlight%28x%29will the border be?

 (9-2x)(25-2x)  = 57ft^2

 9*25 - 68x + 4x^2  = 57

        4x^2 - 68x +168 = 0

         x^2 - 17x + 42  = 0

Factoring

      (x - 14)(x-3) = 0

               x = 3' the width of the border.  (throwing out 14 for the border)

CHECKING our Answer***

        3 * 19 = 57ft^2