SOLUTION: Quilt Dimensions.
Michelle is making a quilt for a wall hanging at the entrance
of a state museum. The finished quilt will measure 8 ft by 6
ft. The quilt has a border of unif
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Michelle is making a quilt for a wall hanging at the entrance
of a state museum. The finished quilt will measure 8 ft by 6
ft. The quilt has a border of unif
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Question 1148928: Quilt Dimensions.
Michelle is making a quilt for a wall hanging at the entrance
of a state museum. The finished quilt will measure 8 ft by 6
ft. The quilt has a border of uniform width around it. The
area of the interior rectangular section is one half the area of the entire quilt. How wide is the border? Found 2 solutions by josgarithmetic, ikleyn:Answer by josgarithmetic(39617) (Show Source):
You can put this solution on YOUR website! x, the uniform border width
, whole quilt area
, inner rectangular area
---------solve for x.
Let "w" be the width of the border, now unknown.
The exterior dimensions are 6 ft by 8 feet with the area 48 sq.feet.
The interior dimensions are (8-2w) ft by (6-2w) ft with the area (6-2w)*(8-2w) sq.feet.
We are given
(6-2w)*(8-2w) = = 24.
It is your basic equation to find "w".
Simplify and solve
48 - 28w + 4w^2 = 24
4w^2 - 28w + 24 = 0
w^2 - 7w + 6w = 0
(w-1)*(w-6) = 0
Only the root w = 1 makes sense.
ANSWER. The width of the border is 1 ft.
CHECK. (6-2*1)*(8-2*1) = 4*6 = 24 sq.ft, which is half of 48 sq.ft.
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