Directions: Each of the questions given below is followed by three statements. You have to study the question and all the three statements given to decide whether any information provided in the statement(s) is/are redundant and can be dispensed with while answering the given question. What is the area of the given rectangle ? I. Perimeter of the rectangle is $60$ cm. II. Breadth of the rectangle is $12$ cm. III. Sum of two adjacent sides is $30$ cm.

### Concept & Geometric Properties The area of a rectangle requires exactly two independent variables: length ($l$) and breadth ($b$). Area = $$l \times b$$ Perimeter = $$2(l + b)$$ ### Step-by-Step Solution 1. **Analyze Statement II:** Breadth $b = 12$ cm. This is a unique, direct measurement and absolutely required. We now just need the length ($l$). 2. **Analyze Statement I:** Perimeter $= 60 \implies 2(l + b) = 60 \implies l + b = 30$. 3. **Analyze Statement III:** Sum of adjacent sides $= 30 \implies l + b = 30$. 4. Notice that Statement I and Statement III provide the exact same mathematical equation ($l + b = 30$). 5. By substituting $b = 12$ from Statement II into this equation, we can find $l = 18$. The area can then be calculated ($18 \times 12$). 6. Because Statements I and III are identical in meaning, we only need one of them alongside Statement II. Therefore, either Statement I or Statement III is redundant. ### Exam Strategy & Shortcut Translate word statements into algebraic equations immediately. When you write out "Perimeter $= 60$" as $l + b = 30$ and "Sum of adjacent sides $= 30$" as $l + b = 30$, it becomes instantly visible that they are duplicate clues. ### Common Pitfall Selecting "I only" or "III only" instead of "I or III only". Since they carry identical information, removing *either* one leaves you with enough data, meaning the redundancy applies to the choice between them, not one specifically. ### Final Answer Therefore, the correct answer is **I or III only**.