SOLUTION: A gardener has a 40 foot by 35 foot rectangular plot of ground. She wants to build a brick walkway of uniform width on the border of the plot. If the gardener wants to have 1,000 s

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Question 1155872: A gardener has a 40 foot by 35 foot rectangular plot of ground. She wants to build a brick walkway of uniform width on the border of the plot. If the gardener wants to have 1,000 square feet of ground left for planting, how wide (to two decimal places) should she build the walkway?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +w+ = the width of the walkway
-------------------
+%28+40+-+2w+%29%2A%28+35+-+2w+%29+=+1000+
+1400+-+70w+-+80w+%2B+4w%5E2+=+1000+
+4w%5E2+-+150w+%2B+400+=+0+
+2w%5E2+-+75w+%2B+200+=+0+
+w+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
+a+=+2+
+b+=+-75+
+c+=+200+
+w+=+%28-%28-75%29+%2B-+sqrt%28+%28-75%29%5E2-4%2A2%2A200+%29%29%2F%282%2A2%29+
+w+=+%28+75+%2B-+sqrt%28+5625+-+1600+%29%29+%2F+4+
+w+=+%28+75+%2B-+sqrt%28+4025+%29%29+%2F+4+
+w+=+%28+75+-+63.4429%29+%2F+4+
+w+=+11.5571+%2F+4+
+w+=+2.889+
the width is 2.89 ft, rounded off.
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check:
+2w%5E2+-+75w+%2B+200+=+0+
+2%2A2.889%5E2+-+75%2A2.889+%2B+200+=+0+
+2%2A8.346321+-+216.675+%2B+200+=+0+
+16.692642+-+216.675+%2B+200+=+0+
+692642+-+.675+=+-.0176+
I think the error is due to rounding off
You can verify this.
Get a 2nd opinion, too, if needed