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?

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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'#.