The length of a rectangle is 4 meters less than twice the width. If the area of the rectangle is 286 square meters, find the dimensions. The width is $\square$ meters. The length is $\square$ meters.
Solution
Step 1 ：Given that the length of a rectangle is 4 meters less than twice the width, we can express this as \(l = 2w - 4\).
Step 2 ：We are also given that the area of the rectangle is 286 square meters. The area of a rectangle is calculated by multiplying the length by the width, so we can express this as \(lw = 286\).
Step 3 ：We now have a system of two equations, which we can solve to find the values of \(w\) and \(l\).
Step 4 ：Solving this system of equations gives us two possible solutions: \((-11, -26)\) and \((13, 22)\).
Step 5 ：However, the dimensions of a rectangle cannot be negative, so we discard the first solution and take the second solution as the correct one.
Step 6 ：This means the width of the rectangle is 13 meters and the length is 22 meters.
Step 7 ：Final Answer: The width is \(\boxed{13}\) meters. The length is \(\boxed{22}\) meters.
