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LUCKY_DIMON [66]
3 years ago
14

Una piscina rectangular de 15 metros de largo por 9 metros de ancho està rodeada por un

Mathematics
1 answer:
stira [4]3 years ago
8 0

Answer: 2 meters.

Step-by-step explanation:

Let w = width of the cement path.

Dimensions of pool : Length = 15 meters , width = 9 meters

Area of pool = length x width = 15 x 9 = 135 square meters

Along width cement path, the length of region = 2w+15

width = 2w+9

Area of road with pool =  (2w+15) (2w+9)

= 4w^2+30w+18w+135\\\\=4w^2+48w+135

Area of road = (Area of road with pool ) -(area of pool)

\Rightarrow\ 112 =4w^2+48w+135- 135\\\\\Rightarrow\ 112= 4w^2+48w\\\\\Rightarrow\ 4 w^2+48w-112=0\\\\\Rightarrow\ w^2+12w-28=0\ \ \ [\text{Divide both sides by 4}]\\\\\Rightarrow\ w^2+14w-2w-28=0\\\\\Rightarrow\ w(w+14)-2(w+14)=0\\\\\Rightarrow\ (w+14)(w-2)=0\\\\\Rightarrow\  w=-14\ or \ w=2

width cannot be negative, so w=2 meters

Hence, the width of the road = 2 meters.

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