SOLUTION: My problem is as follows, a swimming pool 6 meters wide and 10 meters long is to be surrounded by a walk of uniform width. The area of the walk happens to equal the area of the po

Algebra ->  Rectangles -> SOLUTION: My problem is as follows, a swimming pool 6 meters wide and 10 meters long is to be surrounded by a walk of uniform width. The area of the walk happens to equal the area of the po      Log On


   



Question 389785: My problem is as follows, a swimming pool 6 meters wide and 10 meters long is to be surrounded by a walk of uniform width. The area of the walk happens to equal the area of the pool. What is the with of the walk?
Found 2 solutions by scott8148, josmiceli:
Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
the width of the walk is added to both ends of the length and width of the pool
this makes the dimensions of the pool/walk 6+2w by 10+2w
the area is twice the area of the pool ___ a = 6 * 10 * 2 = 120

(6 + 2w)(10 + 2w) = 120

4w^2 + 32w + 60 = 120

w^2 + 8w - 15 = 0

use quadratic formula to find w

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let x = the width of the walk
The area of the swimming pool is 6%2A10+=+60 m2
The walk has the same area
Therefore the area of the pool plus the area of the walk
is 2%2A60+=+120 m2
Each side of the pool is increased by 2x
%286+%2B+2x%29%2A%2810+%2B+2x%29+=+120
60+%2B+20x+%2B+12x+%2B+4x%5E2+=+120
4x%5E2+%2B+32x+-+60+=+0
x%5E2+%2B+8x+-+15+=+0
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
a+=+1
b+=+8
c+=+-15
x+=+%28-8+%2B-+sqrt%28+8%5E2-4%2A1%2A%28-15%29+%29%29%2F%282%2A1%29+
x+=+%28-8+%2B-+sqrt%28+64+%2B+60+%29%29%2F2+
x+=+%28-8+%2B+sqrt%28124%29%29%2F2
x+=%28+-8+%2B+11.136%29%2F2
x+=+3.136%2F2
x+=+1.568
The width of the walk is 1.568 m
check answer:
%286+%2B+2x%29%2A%2810+%2B+2x%29+=+120
%286+%2B+3.136%29%2A%2810+%2B+3.136%29+=+120
9.136%2A13.136+=+120
12.272%2A16.272+=+120
120.010+=+120
close enough