Answer: The length is 13 inches and the width is 5 inches.
Step-by-step explanation:
Ok as we know length times width equals area. That would be l×w=65 for this. We know l is w+8 so we can make this equation
[tex]w(w+8)=65[/tex]
Now we can solve it.
First distributive property
[tex](w)(w)+(w)(8)=65\\\\w^2+8w=65[/tex]
Now subtract 65 from both sides of the equation
[tex]w^2+8w-65=65-65\\w^2+85-65=0[/tex]
Now factor the left side of the equation
(w-5)(w+13)=0
one of the values in the parenthesis has to be 0 to cancel the other one into 0 meaning that w can either be 5 or -13.
Since we are finding area we can't have a negative value so w is 5.
Since the length is 8 more than the width it is 13.
