The area of the rectangle is 54 m squared and the length of the rectangle is 3 meters more than twice the width. what is the length and the width?

We know that the area of a rectangle is solved via the equation:



And we are told that the area of the rectangle is 54, so:



We are told that the length is 3 meters more than twice the width, so we can then set up the equation:

, with w representing the width of the rectangle

Let's plug the above equation into the equation representing area:



Simplify the right side:



And then subtract 54 from both sides to set the equation equal to 0 for factoring purposes:

; then factor:



Set each term equal to 0, and solve for w. We get the answers:

and 

Since the width cannot be a negative number, we take the positive value as the true width. Now we know that the width is  meters.

Let's plug this value into the equation for the length:





So now we know that the length is 12 meters.

Overall, the length of the rectangle is 12 meters and the width of the rectangle is  meters.