SOLUTION: A rectangular field with an area of 8000m^ is enclosed by 400m of fencing. Determine the dimensions of the field to the nearest tenth of a metre.

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Question 1097710: A rectangular field with an area of 8000m^ is enclosed by 400m of fencing. Determine the dimensions of the field to the nearest tenth of a metre.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +W+ = the width of the field
Let +L+ = the length of the field
+2L+%2B+2W+=+400+
+2L+=+400+-+2W+
+L+=+200+-+W+
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Now I can say:
+W%2A%28+200+-+W+%29+=+8000+
+-W%5E2+%2B+200W+-+8000+=+0+
Use qudratic formula
+W+=+%28+-b+%2B-sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29%2F%282a%29+
+a+=+-1+
+b+=+200+
+c+=+-8000+
+W+=+%28+-200+%2B-sqrt%28+40000+-+4%2A%28-1%29%2A%28-8000%29+%29%29%2F%282%2A%28-1%29%29+
+W+=+%28+-200+%2B-sqrt%28+40000+-+32000+%29%29%2F%28-2%29+
+W+=+%28+-200+%2B-sqrt%28+8000+%29+%29+%2F%28-2%29+
+W+=+%28+-200+%2B+89.443+%29+%2F+%28-2%29+
This solution doesn't work since you end up with negative answer, so
+W+=+%28+-200+-+89.443+%29+%2F+%28-2%29+
+W+=+%28+-289.443+%29+%2F+%28-2%29+
+W+=+144.7+
+L+=+200+-+W+
+L+=+200+-+144.7+
+L+=+55.3+
The field is 55.3 by 144.7
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Check answer:
+L%2AW+=+8000+
+55.3%2A144.7+=+8000+
+8001.91+=+8000+
Error due to rounding off, think
also:
+2W+%2B+2L+=+400+
+2%2A144.7+%2B+2%2A55.3+=+400+
+289.4+%2B+110.6+=+400+
+400+=+400+
OK