The area of a rectangle is 60 inches squared and the length of the rectangle is 7 inches longer than the width. the area of a rectangle is found by multiplying the length times the width

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 :)

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