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?

Question

6539 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-08-18T15:35:52

The width of the border is #3'#.

Let the width of the border be #w# feet.

Since the room is #25'# long, the length of the rug must be

25-w (i.e, width of border on one end)-w (i.e., width of border on the other end)#=(25-2w)#

On the same lines, the breadth of the rug must be #(9-2w)#.

Hence, the area of the rug#=(25-2w)(9-2w)#, given to be #57#.

#:. (25-2w)(9-2w)=57#

#:. 225-68w+4w^2-57=0#

#:. 4w^2-68w=57-225=-168#. Completing the square on
the L.H.S., we have,

#:. 4w^2-68w+17^2=289-168=121#

#:. (2w-17)^2=11^2#

#:. 2w-17=+-11#

#:. 2w=17+-11=28, or, 6#

#:. w=14, or, 3#

But, #w=14# will make the breadth of the rug#=-19#, which is not possible.

Hence, the width of the border is #3'#.