SOLUTION: a pool measuring 20 meters by 30 meters is surrounded by a path of uniform width. If the area of the pool and the path combined is 1344 square meters, what is the width of the path

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Question 316794: a pool measuring 20 meters by 30 meters is surrounded by a path of uniform width. If the area of the pool and the path combined is 1344 square meters, what is the width of the path?
Found 2 solutions by checkley77, mananth:
Answer by checkley77(12844) About Me  (Show Source):
You can put this solution on YOUR website!
20*30=600 area of the pool.
(20+2x)(30+2x)=1,344
600+60x+40x+100=1,344
4x^2+100x+600-1,344=0
4x^2+100x-744=0
4(x^2+25x-186)=0
4(x-6)(x+31)=0
x-6=0
x=6 width of the path.
Proof:
(20+2*6)(30+2*6)=1,344
32*42=1,344
1,344=1,344

Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
let the width of the path be x
..
length of pool = 30
width of pool =20
..
length of pool +path width = 30 +2x
width of pool + path width = 20+2x
..
Area = L*W
Area of total plot = (2x+30) * (2x+20)
Area of pool without the path = 30*20 = 600sq.meters
..
(2x+30) * (2x+20) = 1344
4x^2+40x+60x+600=1344
4x^2+100x-744=0
x^2+25x-186=0
x^2+31x-6x-185=0
x(x+31)-6(x+31)=0
(x+31)(x-6)=0
so x= 6 the width of the path