SOLUTION: The Brown Family wants to carpet their livig room, which is 13 ft. by 16 ft. They want a border of uniform width of wood floor to show around the carpet. How wide should the bord

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Question 816: The Brown Family wants to carpet their livig room, which is 13 ft. by 16 ft.
They want a border of uniform width of wood floor to show around the carpet. How wide should the border be if they can afford to carpet only 108 sq. ft?
Please tell me in steps how to solve this.
Thanks
Answer by pushpaharan(47) About Me  (Show Source):
You can put this solution on YOUR website!
Let width of the border be x.
Therefore width of the carpet will be 13-2x (you have to subtract both sides)
Similarly length will be 16-2x.
Therefore area of the carpet = (16-2x)(13-2x) = 108
208 - 58x + 4x^2 = 108
4x^2 - 58x +100 = 0
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
Where a=4, b=-58, c=100
x=-2 or 12.5
But you know width of the border cannot be 12.5 because the width of the floor is only 13.
Therefore width of the border is 2 ft.
Hope you will understand