Answer: Length = 28 feet and width = 9 feet
Step-by-step explanation:
Let x = width of the wall.
Then, Length of the wall = 10+2x
Since , Area of rectangle = length x width
Then, as per given,
[tex]252= (10+2x)x\\\\\Rightarrow\ 252=10x+2x^2\\\\\Rightarrow\ 2x^2+10x-252=0\\\\\Rightarrow\ x^2+5x-126=0\\\\\Rightarrow\ x^2+14x-9x-126=0\\\\\Rightarrow\ (x+14)-9(x+14)=0\\\\\Rightarrow\ (x+14)(x-9)=0\\\\\Rightarrow\ x=-14 \ or \ x= 9[/tex]
Since width cannot be negative , so x = 9
So width = 9 feet and length = 10+2(9)=10+18 = 28 feet
Hence, length is 28 feet and width is 9 feet of the wall of the barn.
