SOLUTION: A pool measures 10 meters by 20 meters is surrounded by a path of uniform width. If the area of the pool and the path combined is 600 square meters, what is the width of the path?

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Question 395871: A pool measures 10 meters by 20 meters is surrounded by a path of uniform width. If the area of the pool and the path combined is 600 square meters, what is the width of the path?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!

Let x = width of the path
The dimensions of the pool + path are
%2820+%2B+2x%29%2A%2810+%2B+2x%29+=+600
200+%2B+60x+%2B+4x%5E2+=+600
4x%5E2+%2B+60x+-+400+=+0
x%5E2+%2B+15x+-+100+=+0
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
a+=+1
b+=+15
c+=+-100
x+=+%28-15+%2B-+sqrt%28+15%5E2-4%2A1%2A%28-100%29+%29%29%2F%282%2A1%29+
x+=+%28-15+%2B-+sqrt%28+225+%2B+400+%29%29%2F2+
x+=+%28-15+%2B+25%29%2F2+
x+=+5
and
x+=+%28-15+-+25%29%2F2+ (can't use a negative result)
The width of the path is 5 m
check answer:
%2820+%2B+2x%29%2A%2810+%2B+2x%29+=+600
%2820+%2B+10%29%2A%2810+%2B+10%29+=+600
30%2A20+=+600