Answer:
[tex]Length=7units\\\\Width=5units[/tex]
Step-by-step explanation:
Width=(Length-2) units
W=(L-2) units
Area of the rectangle= 35 square units
Area = length* Width
[tex]35= L*(L-2)\\\\35=L^2-2L[/tex]
Subtracting 35 both sides:
[tex]L^2-2L-35=0[/tex]
Solving the quadratic equation for 'L' ;
Using factorization:
[tex]L^2+5L-7L-35=0[/tex]
Taking common from the equation :
[tex]L(L+5)-7(L+5)=0\\\\(L+5)(L-7)=0\\\\L+5=0\\\\L=-5[/tex]
OR
[tex]L-7=0\\\\L=7[/tex]
The length cannot be negative, therefore Length(L)= 7
[tex]Width=Length-2\\\\=7-2\\\\=5 units[/tex]
[tex]Length=7units\\\\Width=5units[/tex]
