SOLUTION: In order to double the carpeted area in an office lobby,a decorator adds a strip of carpet on all 4 sides of a 4yd. by 6 yd. rectangle that is now carpeted. How wide is the strip

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Question 1138281: In order to double the carpeted area in an office lobby,a decorator adds a strip of carpet on all 4 sides of a 4yd. by 6 yd. rectangle that is now carpeted.
How wide is the strip?

Found 3 solutions by greenestamps, josgarithmetic, josmiceli:
Answer by greenestamps(13208) About Me  (Show Source):
You can put this solution on YOUR website!


The current carpeted area is 4x6 = 24 square yards.

The area doubled will be 24*2 = 48 square yards.

The original length is 2 more than the width; assuming the added strip is of uniform width, the new length still has to be 2 more than the width. Two numbers that differ by 2 and have a product of 48 are 6 and 8. So the new overall dimensions are 6x8 yards.

Since the length and width have each increased by 2 yards, and the added carpet is on all four sides, the width of the strip is 1 yard.

Answer by josgarithmetic(39629) About Me  (Show Source):
You can put this solution on YOUR website!
2%2A%284%2A6%29=%282x%2B4%29%282x%2B6%29
Simplify and solve for x.

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2%2A4%2A6=2%2A2%2A%28x%2B2%29%28x%2B3%29
12=%28x%2B2%29%28x%2B3%29, factors of 12 differ by 1.
12=3%2A4
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system%28x%2B2=3%2Cx%2B3=4%29
highlight_green%28x=1%29

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +x+ = the widths of the added strips
+2x+ = the width that is added to the sides
convert yards to feet
+12+%2B+2x+%29%2A%28+18+%2B+2x+%29+=+2%2A12%2A18+
+216+%2B+36x+%2B+24x+%2B+4x%5E2+=+432+
+4x%5E2+%2B+60x+-+216+=+0+
+x%5E2+%2B+15x+-+54+=+0+
Use quadratic formula
+x+=+%28-15+%2B-+sqrt%28+15%5E2-4%2A1%2A%28-54%29+%29%29%2F%282%2A1%29+
+x+=+%28-15+%2B-+sqrt%28+225+%2B+216+%29%29%2F2+
+x+=+%28+-15+%2B+sqrt%28+441+%29+%29%2F2+
+x+=+%28+-15+%2B+21+%29%2F2+
+x+=+3+ ft
This is 1 yd so the strip is 1 yd wide.
I converted to feet thinking there might
be fractions of a yd in answer
--------------------------------------------
check:
+%28+12+%2B+2x+%29%2A%28+18+%2B+2x+%29+=+432+
+%28+12+%2B+2%2A3+%29%2A%28+18+%2B+2%2A3+%29+=+432+
+18%2A24+=+432+
+432+=+432+
OK