A carpenter is designing a table. The table will be in the form of a rectangle whose length is 4 feet more than its width. How long should the table be if the carpenter wants the area of the table to be 45 sq ft? (J.M.E.T., 2010)

### Concept & Algebra Translate the given word problem into algebraic equations. We need to find the dimensions using the area of a rectangle. $$ \text{Area} = \text{length} \times \text{width} $$ ### Step-by-Step Solution * Let the width of the table be $w$ feet. * The length is 4 feet more than the width, so length $l = w + 4$. * The area is given as 45 sq ft, which yields the equation: $$ w(w + 4) = 45 $$ * Expanding this gives a quadratic equation: $$ w^2 + 4w - 45 = 0 $$ * Factoring the quadratic equation: $$ (w + 9)(w - 5) = 0 $$ * Since a dimension cannot be negative, $w = 5$ feet. * The question asks for the length of the table: $l = w + 4 = 5 + 4 = 9$ feet. ### Exam Strategy & Shortcut Instead of solving the quadratic equation, use the options! The question asks for the length. Test Option (b): If length = 9, then width = 9 - 4 = 5. Area = $9 \times 5 = 45$. This matches the condition perfectly. ### Common Pitfall A common mistake is solving for the width ($w = 5$) and assuming that is the final answer. Always re-read the question to check what specific value is being asked for (in this case, "How long", meaning length). ### Final Answer Therefore, the correct answer is **9 ft**.