SOLUTION: A vacant lot is being converted into a community garden. The garden and the walkway around its perimeter have an area of 550 ft2. Find the width of the walkway if the garden is 12

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: A vacant lot is being converted into a community garden. The garden and the walkway around its perimeter have an area of 550 ft2. Find the width of the walkway if the garden is 12       Log On


   



Question 1046118: A vacant lot is being converted into a community garden. The garden and the walkway around its perimeter have an area of 550 ft2. Find the width of the walkway if the garden is 12 ft wide by 15 ft long.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let the width of the walkway = +x+ ft
+%28+12+%2B+2x+%29%2A%28+15+%2B+2x+%29+=+550+
Note that you have to add +x+ on BOTH sides
of the length and width
+180+%2B+30x+%2B+24x+%2B+4x%5E2+=+550+
+4x%5E2+%2B+54x+-+370+=+0+
+2x%5E2+%2B+27x+-+185+=+0+
use quadratic formula
+x+=+%28+-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+
+a+=+2+
+b+=+27+
+c+=+-185+
+x+=+%28+-27+%2B-+sqrt%28+27%5E2+-+4%2A2%2A%28-185%29+%29%29+%2F+%282%2A2%29+
+x+=+%28+-27+%2B-+sqrt%28+729+%2B+1480+%29%29+%2F+4+
+x+=+%28+-27+%2B-+sqrt%28+2209+%29%29+%2F+4+
+x+=+%28+-27+%2B+47+%29+%2F+4+
+x+=+20%2F4+
+x+=+5+
The width of the walkway is 5 ft
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check:
+%28+12+%2B+2x+%29%2A%28+15+%2B+2x+%29+=+550+
+%28+12+%2B+2%2A5+%29%2A%28+15+%2B+2%2A5+%29+=+550+
+%28+12+%2B+10+%29%2A%28+15+%2B+10+%29+=+550+
+22%2A25+=+550+
+550+=+550+
OK