Answer:
[tex]Original\ length\ of\ square=10\ inches[/tex]
Step-by-step explanation:
Let the length of square [tex]=x\ inches[/tex]
[tex]8[/tex] inches is added one side of square
Then length of one side [tex]=x+8\ inches[/tex]
[tex]3\ inches[/tex] is subtracted other side of square
Then length of other side [tex]=x-3[/tex]
[tex]area\ of square =126\ inches^2\\\\Side\times side =126\ inches^2\\\\(x+8)\times(x-3)=126\ inches^2\\\\x(x-3)+8(x-3)=126\ inches^2\\\\x^2-3x+8x-24=126\ inches^2\\\\x^2+5x-24=126\ inches^2\\\\x^2+5x-150=0\\\\x^2+15x-10x-150=0\\\\x(x+15)-10(x+15)=0\\\\(x+15)(x-10)=0\\\\x+15=0\\x=-15\ \ \ \ negative\ length\ does\ not\ consider\\\\x-10=0\\x=10[/tex]
[tex]Original\ length\ of\ square\ =10\ inches[/tex]
