If the length of a rectangle is 3 feet less then twice its width and the area is 54square feet what are its dimensions

The length (L) of the rectangle can be written as a function of the width (W):
Now since we know Area = Width*Length, we can write the area as a function of the width:

Distributing the W inside the parentheses we have:

We know the area is 54 ft^2, so we can rewrite it as:

Now solve for W by factoring (or by applying the quadratic formula):

Factor out a common 2W from the first two terms and a 9 from the last two terms:

Regroup the terms to get our fully factored equation:

This gives us the roots W = 6 and W = -9/2, but width can't be negative so we have width = 6 ft. Then remember that the length L = 2W - 3, so our length is:

So now we know that our rectangle is 9 feet long and 6 feet wide.