Answer:
[tex]Length=9 units\\width=8 units[/tex]
Step-by-step explanation:
Width of the rectangle= W
Length= L
W=(L-1) units
Area= 72 square units
Area of a rectangle= Length*Width
[tex]72=L*(L-1)\\\\72=L^2-L\\\\L^2-L-72=0[/tex]
Solving the quadratic equation using the factorization method:
[tex]L^2+8L-9L-72=0[/tex]
Taking common from the equation:
[tex]L(L+8)-9(L+8)=0\\(L+8)(L-9)=0[/tex]
[tex]L+8=0\\L=-8[/tex]
OR
[tex]L-9=0\\L=9[/tex]
The length cannot be negative, therefore: Length= 9 units
[tex]Width=Length-1\\=9-1\\=8 units[/tex]
[tex]Length=9 units\\width=8 units[/tex]
