In order to answer a question like this, we have to create an equation to solve it.
A=lw is the area of a rectangle. We've been given the value of the area,
60=lw
We've also been given that the length is 7 inches longer than the width meaning that,
l=w+7
The equation above means that "length equals width plus 7 inches"
We now have to value of l so we can substitute that in to our original equation
60=(w+7)w
Expand,
60=w^2+7w
Subtract both sides by 60
w^2+7w-60=0
From here we can factor w^2+7w-60 and turn it into a multiplication statement
(w+12)(w-5)=0
We see that in order to have an answer of 0, w must equal -12 or 5. However we cannot use -12 as our width since there is no such thing as a negative length/width. Therefore, our width is 5.
Now that we have the value of the width,
l=w+7
Since w=5
l=5+7
l=12
Therefore, the length of the rectangle is 12 inches and the width is 5 inches.
We can check this answer by putting it into the formula of the area
60=lw
l=12 and w=5
60=12x5
60=60
And the length is greater than the width by 7 inches.
Hope this helps :)
