SOLUTION: A rectangle flower garden, 7m by 6 m, is surrounded by a grass strip of uniform width. If the total area of the garden and the grass strip is 90m, what is the width of the strip?

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Question 110788: A rectangle flower garden, 7m by 6 m, is surrounded by a grass strip of uniform width. If the total area of the garden and the grass strip is 90m, what is the width of the strip?
Answer by MathLover1(3376) About Me  (Show Source):
You can put this solution on YOUR website!
A rectangle flower garden, 7m by 6 m, is surrounded by a grass strip of uniform width. If the total area of the garden and the grass strip is 90m, what is the width of the strip?
Given:
Length+=+L+=+7m+
Width+=+W+=+6+m
total_+area+=+A%5B3%5D++=+90m%5E2
Then:
total_+area++=+are_of_rectangle++-plus_+a_+grass_+strip+_+area=+A }}}
A+=+%287%2B+G%29%286+%2B+G%29
0r
90=+%287%2B+G%29%286+%2B+G%29
+90=+42+%2B+7G+%2B+6G+%2B+G%5E2+
+90=++42+%2B+13G++%2B+G%5E2+
+G%5E2+%2B+13G++%2B+42+%96+90+=+0
+G%5E2+%2B+13G+++%96+48+=+0
Solve for G using quadratic formula:
+G%5B1%2C2%5D+=%28-b+%2B-+sqrt+%28b%5E2+-4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29
+G%5B1%2C2%5D+=%28-13+%2B-+sqrt+%2813%5E2+-+4%2A1%2A%28-48%29+%29%29+%2F+%282%2A1%29
+G%5B1%2C2%5D+=%28-13+%2B-+sqrt+%28169+%2B++192%29%29+%2F+%282%29
+G%5B1%2C2%5D+=%28-13+%2B-+sqrt+%28361%29%29+%2F+%282%29
+G%5B1%2C2%5D+=%28-13+%2B-+19%29+%2F+%282%29
We need only positive root:
+G%5B1%2C2%5D+=%28-13+%2B+19%29+%2F+2
+G%5B1%2C2%5D+=+6+%2F+2
+G%5B1%2C2%5D+=+3m
Check:
90m%5E2=+%287m%2B+Gm%29%286m+%2B+Gm%29
90m%5E2=+%287m+%2B+3m%29%286m+%2B+3m%29
90m%5E2=+10m%2A9m
90m%5E2=+90m%5E2