SOLUTION: Nick has a beautiful rectangular garden, which measures 3 m by 3 m. He wants to create a uniform border of river rocks around three sides of his garden. If he wants the area of the

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Question 433556: Nick has a beautiful rectangular garden, which measures 3 m by 3 m. He wants to create a uniform border of river rocks around three sides of his garden. If he wants the area of the border and the area of his garden to be equal, how wide should the border be?
I've got a length of 9 - 2w. And a width of 4.5 However my textbook's got an answer of 0.84 m.
Please clarify as to what I've done incorrectly by showing all steps.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let w = the width of the border
given:
the area of the garden is 3%2A3+=+9 m2
The dimensions of the garden plus the border are
+%283+%2B+2w%29%2A%283+%2B+w%29+
+%283+%2B+2w%29%2A%283+%2B+w%29++=+9+%2B+6w+%2B+3w+%2B+2w%5E2+
+2w%5E2+%2B+9w+%2B+9+=+2%2A9+
+2w%5E2+%2B+9w+-+9+=+0
use the quadratic formula
w+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
a+=+2
b+=+9
c+=+-9
w+=+%28-9+%2B-+sqrt%28+9%5E2-4%2A2%2A%28-9%29+%29%29%2F%282%2A2%29+
w+=+%28-9+%2B-+sqrt%28+81+%2B+72+%29%29%2F4+
w+=+%28-9+%2B-+sqrt%28+153+%29%29%2F4+
w+=+%28-9+%2B+12.369%29%2F4+
+w+=+3.369%2F4+
+w+=+.842+ m