SOLUTION: A swimming pool is 5 m longer than it is wide and is surrounded by a deck 2 m wide. The area of the pool and deck together is at least 140m^2 greater than the area of the pool alon

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Question 897639: A swimming pool is 5 m longer than it is wide and is surrounded by a deck 2 m wide. The area of the pool and deck together is at least 140m^2 greater than the area of the pool alone. What can you conclude about the dimensions of the pool?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +p+ = area of the pool in m2
Let +d+ = area of the deck in m2
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given:
+p+%2B+d+=+p+%2B+140+ m2
The area of the pool plus the deck is:
+p+%2B+d+=+%28+w+%2B+2+%29%2A%28+w+%2B+7+%29+
+%28+w+%2B+2+%29%2A%28+w+%2B+7+%29+=+p+%2B+140+
+p+=+%28+w+%2B+2+%29%2A%28+w+%2B+7+%29+-+140+
The width has to be greater than +7.594++ m
The length is greater than +12.594+ m
since
+w%5E2+%2B+9w+%2B+14+=+140+
+w%5E2+%2B+9w+-+126+=+0+
+w+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
+a+=+1+
+b+=+9+
+c+=+-126+
+w+=+%28+-9+%2B-+sqrt%28+9%5E2+-+4%2A1%2A%28-126%29+%29%29%2F%282%2A1%29+
+w+=+%28+-9+%2B-+sqrt%28+81+%2B+504+%29%29+%2F+2+
+w+=+%28+-9+%2B+sqrt%28+585+%29+%29+%2F+2+
+w+=+%28+-9+%2B+24.187+%29+%2F+2+
+w+=+15.187+%2F+2+
+w+=+7.594+
----------------
check:
+w%5E2+%2B+9w+%2B+14+=+140+
+7.594%5E2+%2B+9%2A7.594+%2B+14+=+140+
+57.661+%2B+68.3415+%2B+14+=+140+
+140.0025+=+140++
close enough