SOLUTION: A floor plan shows that the exterior of a room has dimensions 12 feet by 17 feet. If the area of the room measured from the interior is only 176 square feet, express the thickness

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Question 1048261: A floor plan shows that the exterior of a room has dimensions 12 feet by 17 feet. If the area of the room measured from the interior is only 176 square feet, express the thickness of the surrounding walls in feet. (Assume that the walls have uniform thickness).

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The walls are of uniform thickness.
Let +x+ = the thickness of the walls
If I subtract +2x+ from each dimesion
of the exterior walls, I will have the
dimensions of the interior walls, so I can say:
+%28+12+-+2x+%29%2A%28+17+-+2x+%29=+176+
+204+-+34x+-+24x+%2B+4x%5E2+=+176+
+4x%5E2+-+58x+%2B+28+=+0+
+2x%5E2+-+29x+%2B+14+=+0+
Use quadratic formula
+x+=+%28+-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+
+a+=+2+
+b+=+-29+
+c+=+14+
+x+=+%28+-%28-29%29+%2B-+sqrt%28+%28-29%29%5E2+-+4%2A2%2A14+%29%29+%2F+%282%2A2%29+
+x+=+%28+29+%2B-+sqrt%28+841+-+112+%29%29+%2F+4+
+x+=+%28+29+%2B-+sqrt%28+729+%29%29+%2F+4+
+x+=+%28+29+-+27+%29%2F4+
+x+=+1%2F2+
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The other possibility is:
+x+=+%28+29+%2B+27+%29%2F4+
+x+=+56%2F4+
+x+=+14+ ( this is impossible, since one wall is 12' long )
------------------
The wall is 6 inches thick ( 1/2 ft )
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check:
+%28+12+-+2x+%29%2A%28+17+-+2x+%29=+176+
+%28+12+-+2%2A.5+%29%2A%28+17+-+2%2A.5+%29=+176+
+%28+12+-+1+%29%2A%28+17+-+1+%29+=+176+
+11%2A16+=+176+
+176+=+176+
OK