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 $3'$ .