SOLUTION: A man built a walk of uniform width around a rectangular pool. If the area of the walk is 315 square feet and the dimensions of the pool are 8 feet by 18 feet, how wide is the walk

Algebra ->  Average -> SOLUTION: A man built a walk of uniform width around a rectangular pool. If the area of the walk is 315 square feet and the dimensions of the pool are 8 feet by 18 feet, how wide is the walk      Log On


   

Question 831455: A man built a walk of uniform width around a rectangular pool. If the area of the walk is 315 square feet and the dimensions of the pool are 8 feet by 18 feet, how wide is the walk? please help!
Found 2 solutions by richwmiller, josmiceli:
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
already answered twice in the last few days

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let x = the width of the walk
The measurement of the shortest side is
+8+%2B+2x+
The measurement of the longest side is
+18+%2B+2x+
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The area of the pool is +8%2A18+=+144+ ft2
The area of the pool plus the walk is
+144+%2B+315+=+459+ ft2
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I can also express the area of the pool plus
the walk as:
+%28+8+%2B+2x+%29%2A%28+18+%2B+2x+%29+, so
+%28+8+%2B+2x+%29%2A%28+18+%2B+2x+%29+=+459+
+144+%2B+36x+%2B+16x+%2B+4x%5E2+=+459+
+4x%5E2+%2B+52x+-+315+=+0+
+x+=+%28+-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+
+a+=+4+
+b+=+52+
+c+=+-315+
+x+=+%28+-52+%2B-+sqrt%28+52%5E2-4%2A4%2A%28-315%29+%29%29+%2F+%282%2A4%29+
+x+=+%28+-52+%2B-+sqrt%28+2704+%2B+5040+%29%29+%2F+8+
+x+=+%28+-52+%2B-+sqrt%28+7744+%29%29+%2F+8+
+x+=+%28+-52+%2B-+88%29+%2F+8+
+x+=+36+%2F+8+ ( can't use the negative square root )
+x+=+4.5+
The width of the walk is 4.5 ft
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check:
+%28+8+%2B+2x+%29%2A%28+18+%2B+2x+%29+=+459+
+%28+8+%2B+2%2A4.5+%29%2A%28+18+%2B+2%2A4.5+%29+=+459+
+%28+8+%2B+9+%29%2A%28+18+%2B+9+%29+=+459+
+17%2A27+=+459+
+459+=+459+