SOLUTION: You have made a quilt that is 3 feet by 4 feet. You want to use the remaining 18 square feet of fabric to add a decorative border of uniform width. What should the width of the bor

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: You have made a quilt that is 3 feet by 4 feet. You want to use the remaining 18 square feet of fabric to add a decorative border of uniform width. What should the width of the bor      Log On


   



Question 898084: You have made a quilt that is 3 feet by 4 feet. You want to use the remaining 18 square feet of fabric to add a decorative border of uniform width. What should the width of the border be? Please help !
Found 2 solutions by josmiceli, josgarithmetic:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +x+ = the width of the uniform border
+x+ gets added twice to both dimensions, so
I can say:
+3%2A4+%2B+18+=+%28+3+%2B+2x+%29%2A%28+4+%2B+2x+%29+
+30+=+12+%2B+8x+%2B+6x+%2B+4x%5E2+
+4x%5E2+%2B+14x+-+18+=+0+
+2x%5E2+%2B+7x+-+9+=+0+
-----------------------
Use the quadratic formula:
+x+=+%28+-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+
+a+=+2+
+b+=+7+
+c+=+-9+
+x+=+%28+-7+%2B-+sqrt%28+7%5E2+-+4%2A2%2A%28-9%29+%29%29+%2F+%282%2A2%29+
+x+=+%28+-7+%2B-+sqrt%28+49+%2B+72+%29%29+%2F+4+
+x+=+%28+-7+%2B+sqrt%28+121+%29%29+%2F+4+
+x+=+%28+-7+%2B+11+%29+%2F+4+
+x+=+4%2F4+
+x+=+1+
The width of the border is 1 ft
check:
+30+=+12+%2B+8x+%2B+6x+%2B+4x%5E2+
+30+=+12+%2B+8%2A1+%2B+6%2A1+%2B+4%2A1+
+30+=+12+%2B+8+%2B+6+%2B+4+
+30+=+30+
OK

Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
The only sense I can make here is that the quilt made covers 3 feet by 4 feet, leaving a path around the quilt on the piece of material unquilted.

x and y, the dimensions of quilted part
w, the width around the quilted part
expect x=3 and y=4.

Total Material Area, %28x%2B2w%29%28y%2B2w%29
Quilted Area, xy
Unquilted Area, %28x%2B2w%29%28y%2B2w%29-xy
The unquilted area is given as 18 square feet to be used for decorative border.

Meaning is %28x%2B2w%29%28y%2B2w%29-xy=18.
xy%2B2yw%2B2xw%2B4w%5E2-xy=18
2yw%2B2xw%2B4w%5E2=18
4w%5E2%2B2w%28x%2By%29=18
2w%5E2%2Bw%28x%2By%29=9
2w%5E2%2Bw%28x%2By%29-9=0
Substitute the given or expected values x and y,
highlight_green%282w%5E2%2B7w-9=0%29
%282w%2B9%29%28w-1%29=0
Choose the factor which has a meaningful solution.
highlight%28w=1%29.

Border will be a uniform ONE FOOT Width.