SOLUTION: You have made a quilt that is 4 feet by 5 feet. You want to use the remaining 10 square feet of fabric to add a decorative border of uniform width. Part a: Write a quadratic e

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: You have made a quilt that is 4 feet by 5 feet. You want to use the remaining 10 square feet of fabric to add a decorative border of uniform width. Part a: Write a quadratic e      Log On


   



Question 961186: You have made a quilt that is 4 feet by 5 feet. You want to use the remaining 10 square feet of fabric to add a decorative border of uniform width.

Part a: Write a quadratic equation set equal to zero that you could use to determine the width of the border .
Part b: The width of the border should be ? feet.
Can i please have help with this?

Found 2 solutions by stanbon, josmiceli:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
You have made a quilt that is 4 feet by 5 feet. You want to use the remaining 10 square feet of fabric to add a decorative border of uniform width.
Part a: Write a quadratic equation set equal to zero that you could use to determine the width of the border .
Length of border = 2(4+5) = 18 feet
Let the width be "x":
Equation:
18x = 10 sq ft
x = 5/9 ft (width of the border
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Part b: The width of the border should be ? feet.
x = 5/9 ft (width of the border
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Cheers,
Stan H.
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Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +x+ = the extra length added to all
4 sides of the quilt
-----------------
One side will now measure +5+%2B+2x+ ft
The other side will measure +4+%2B+2x+ ft
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(a)
The extra area has to add up to +10+ ft2
I can say:
+%28+5+%2B+2x+%29%2A%28+4+%2B+2x+%29+-+4%2A5+=+10+
+20+%2B+8x+%2B+10x+%2B+4x%5E2+-+20+=+10+
+4x%5E2+%2B+18x+-+10+=+0+
+2x%5E2+%2B+9x+-+5+=+0+
--------------------------
(b)
Use the quadratic formula
+x+=+%28+-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+
+a+=+2+
+b+=+9+
+c+=+-5+
+x+=+%28+-9+%2B-+sqrt%28+9%5E2+-+4%2A2%2A%28-5%29+%29%29+%2F+%282%2A2%29+
+x+=+%28+-9+%2B-+sqrt%28+81+%2B+40+%29%29+%2F+4+
+x+=+%28+-9+%2B+11+%29+%2F+4+
+x+=+2+%2F+4+
+x+=+.5+
The width of the border is .5 ft
check:
+%28+5+%2B+2x+%29%2A%28+4+%2B+2x+%29+-+4%2A5+=+10+
+%28+5+%2B+2%2A.5+%29%2A%28+4+%2B+2%2A.5+%29+-+4%2A5+=+10+
+%28+5+%2B+1+%29%2A%28+4+%2B+1+%29+-+20+=+10+
+6%2A5+-+20+=+10+
+30+-+20+=+10+
+10+=+10+
OK
I had to assume a lot here, like the extra fabric
did not get folded, but I think I got what
they were after
Hope this helps