A pool measuring 10 meters by 20 meters is surrounded

Ernest Ryland

Ernest Ryland

Answered question

2021-12-15

A pool measuring 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 & Explanation

Matthew Rodriguez

Matthew Rodriguez

Beginner2021-12-16Added 32 answers

Step 1
Let width of the path be "y" meters
Now combined width and length would be 10+2y and 20+2y.
Now we have
(10+2y)(20+2y)=600
4(5+y)(10+y)=600
Divide both side by 4
(5+y)(10+y)=150
Multipying we get
5(10+y)+y(10+y)=150
50+5y+10y+y^{2}=150
y2+15y100=0
Step 2
Factorization
y2+20y5y100=0
y(y+20)-5(y+20)=0
(y+20)(y-5)=0
y=5,20
Neglect y=-20
Answer
y=5
Thomas Lynn

Thomas Lynn

Beginner2021-12-17Added 28 answers

The total area is 600, so we sum up the parts. There are different ways to break up the parts, but breaking it into 4 corner squares, 4 rectangles on the sides, top and bottom, then the pool itself might be simpler.
600=4x2=2(10x)+2(20x)+10(20)
600=4x2+60x+200
0=4x2+60x400
=x2+15x100
=(x+20)(x-5)
x=-20
x=5
Result:
5 meters

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