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 sqaure meters, what is the width of the path

Question 316864: 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 sqaure meters, what is the width of the path?
Found 2 solutions by palanisamy, mananth:
Answer by palanisamy(496) (Show Source): You can put this solution on YOUR website!
Given, the length of the pool = 30 m
And the width of the pool = 20 m
Let the width of the path = x m
Then, the length of the rectangle including the path = 30+x
And the width of the rectangle including the path = 20+x
Total area is (30+x)(20+x) = 1344
600+30x+20x+x^2-1344 = 0
x^2 +50x-744 = 0
X^2+62x-12x-744=0
x(x+62)-12(x+62)=0
(x-12)(x+62)=0
x=12,-62
The width of the path is 12 m
Answer by mananth(16946) (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 of total plot = 2x+30 * 2x+20
Area of pool = 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
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