Equations and Inequalities Solving a word problem using a quadratic equation with rational roots The area of a rectangle is $54 \mathrm{~m}^{2}$, and the length of the rectangle is $3 \mathrm{~m}$ more than twice the width. Find the dimensions rectangle. Length : $\square \mathrm{m}$ Width : $\square \mathrm{m}$

Step 1 ：We are given that the area of a rectangle is 54 square meters and the length of the rectangle is 3 meters more than twice the width. We need to find the dimensions of the rectangle.

Step 2 ：We can denote the width as 'w' and the length as 'l'.

Step 3 ：From the problem, we have two equations: \(l \times w = 54\) and \(l = 2w + 3\).

Step 4 ：We can substitute the second equation into the first one to solve for 'w', and then substitute 'w' into the second equation to solve for 'l'.

Step 5 ：The solutions for 'w' and 'l' are -6 and 9/2, and -9 respectively. However, the dimensions of a rectangle cannot be negative. Therefore, we discard the negative solutions and take the positive solutions for 'w' and 'l'.

Step 6 ：Final Answer: The dimensions of the rectangle are \(\boxed{9/2 \mathrm{~m}}\) for the width and \(\boxed{9 \mathrm{~m}}\) for the length.