Answer:
[tex]Length= 8m\\\\Width=6m[/tex]
Step-by-step explanation:
Let the length of the rectangle be 'L' meter
Width of the rectangle= (L-2 ) meter
Area of the rectangle= [tex]48 m^2[/tex]
Area of a rectangle = length * width
[tex]48=L*(L-2)\\\\48=L^2-2L\\\\L^2-2L-48=0[/tex]
Making the factors of the equation:
[tex]L^2+6L-8L-48=0\\[/tex]
Taking common form the equation:
[tex]L(L+6)-8(L+6)=0\\\\(L+6)(L-8)=0\\[/tex]
[tex]L+6=0\\\\L=-6[/tex]
OR
[tex]L-8=0\\\\L=8[/tex]
The length of the rectangle cannot be negative, so [tex]Length(L)=8 m[/tex]
[tex]Width=L-2= 8-2= 6 m[/tex]
[tex]Length= 8m\\\\Width=6m[/tex]
