Answer:
Length 7 feet and Width 5 feet
Step-by-step explanation:
we know that
The area of the rectangle ( a dining room table) is equal to
[tex]A=LW[/tex]
where
[tex]L=(3x+1)\ ft[/tex]
[tex]W=(3x-1)\ ft[/tex]
[tex]A=35\ ft^2[/tex]
substitute
[tex]35=(3x+1)(3x-1)[/tex]
Apply difference of squares right side
[tex]35=9x^2-1[/tex]
[tex]9x^2=36\\x^2=4\\x=\pm2[/tex]
Remember that the length cannot be a negative number
so
x=2
Find the length
[tex]L=(3(2)+1)=7\ ft[/tex]
Find the width
[tex]W=(3(2)-1)=5\ ft[/tex]
