Answer:
Explanation:
For this type of question, it helps to draw the rectangle and label its sides. Label the length x. We are given that the width is 5 miles less than the length, which can be represented algebraically as x-5. So, if y = width, then we have y = x-5.
We are also given that the area is 84 square miles, so how do we find the area of a rectangle? The formula is Area = length * width. Substituting in what we know, we get 84 = x(x-5). We distribute on the right hand side to get 84 = x^2-5x, which is equivalent to x^2-5x-84=0. This can be factored as (x-12)(x+7)=84. The solutions are x=12 or x=-7, but we ignore x=-7 because we cannot have negative length. Thus, the length of the rectangle is 12 miles and the width is 12-5=7 miles.