SOLUTION: a rug is to fit a room so that a border of even width is left on all four sides. If the room is 21 by 24 feet and the area of the rug is 238 square feet, how wide will the border b

Algebra ->  Customizable Word Problem Solvers  -> Geometry -> SOLUTION: a rug is to fit a room so that a border of even width is left on all four sides. If the room is 21 by 24 feet and the area of the rug is 238 square feet, how wide will the border b      Log On

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Question 1048668: a rug is to fit a room so that a border of even width is left on all four sides. If the room is 21 by 24 feet and the area of the rug is 238 square feet, how wide will the border be?

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +x+ = the width of the border
+%28+21+-+2x+%29%2A%28+24+-+2x+%29+=+238+
( do you see why I subtracted +2x+ from each dimension ? )
+504+-+48x+-+42x+%2B+4x%5E2+=+238+
+4x%5E2+-+90x+%2B+266+=+0+
+2x%5E2+-+45x+%2B+133+=+0+
Use quadratic formula
+x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
+a+=+2+
+b+=+-45+
+c+=+133+
+x+=+%28-%28-45%29+%2B-+sqrt%28+%28-45%29%5E2-4%2A2%2A133+%29%29%2F%282%2A2%29+
+x+=+%28+45+%2B-+sqrt%28+2025+-+1064+%29%29+%2F+4+
+x+=+%28+45+%2B-+sqrt%28+961+%29%29+%2F+4+
+x+=+%28+45+-+31+%29+%2F+4+ ( only the minus square root works here )
+x+=+14%2F4+
+x+=+7%2F2+
+x+=+3.5+
The border is 3.5 ft wide
-------------------------
check:
+%28+21+-+2x+%29%2A%28+24+-+2x+%29+=+238+
+%28+21+-+2%2A%287%2F2%29+%29%2A%28+24+-+2%2A%287%2F2%29+%29+=+238+
+%28+21+-+7+%29%2A%28+24+-+7+%29+=+238+
+14%2A17+=+238+
+238+=+238+
OK