SOLUTION: A 16 ft by 18 ft rectangular garden is to have a gravel path of uniform width bordering it. How wide is the path if the total area covered by the garden and path is 440 ft2?

Algebra ->  Customizable Word Problem Solvers  -> Geometry -> SOLUTION: A 16 ft by 18 ft rectangular garden is to have a gravel path of uniform width bordering it. How wide is the path if the total area covered by the garden and path is 440 ft2?      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


   



Question 1037981: A 16 ft by 18 ft rectangular garden is to have a gravel path of uniform width bordering it. How wide is the path if the total area covered by the garden and path is 440 ft2?
Found 2 solutions by josgarithmetic, josmiceli:
Answer by josgarithmetic(39617) About Me  (Show Source):
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +w+ = the width in ft of the path
Including the path, the dimensions
of the garden are:
+16+%2B+2w+ and +18+%2B+2w+
The area, +A+, is:
+A+=+%28+16+%2B+2w+%29%2A%28+18+%2B+2w+%29+
+A+=+288+%2B+36w+%2B+32w+%2B+4w%5E2+
+4w%5E2+%2B+68w+%2B+288+=+440+
+4w%5E2+%2B+68w+-+152+
+w%5E2+%2B+17w+-+38+=+0+
+%28+w+%2B+19+%29%2A%28+w+-+2+%29+=+0+ ( by inspection )
+w+=+2+ ( width must be positive )
-------------------------------
The path is 2 ft wide
-------------------------
check:
+A+=+%28+16+%2B+2w+%29%2A%28+18+%2B+2w+%29+
+A+=+%28+16+%2B+2%2A2+%29%2A%28+18+%2B+2%2A2+%29+
+A+=+20%2A22+
+A+=+440+ ft2
OK