Question

The area of a triangle is equal to the area of the rectangle. Find the perimeter of the rectangle.
1. The perimeter of the square is 24 inches.
2. The sum of the length and the width is 13 inches.

• A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
• B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
• C. BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question.
• D. EACH statement ALONE is sufficient to answer the question asked.
• E. Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

Hint:

In Data Sufficiency, focus only on what you need to answer the question. Here, the goal was the perimeter, which is \( 2(l+w) \). Statement (2) directly provides \( (l+w) \), making it sufficient on its own. Don't get distracted by extra, unrelated information.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
The question asks for the perimeter of a rectangle. Data Sufficiency questions test whether the given information is enough to arrive at a single, unique answer. We need to evaluate each statement independently and then together.
Step 2: Key Formula or Approach:
The formula for the perimeter of a rectangle is:
\[ P = 2 \times (length + width) = 2(l + w) \] To find the perimeter, we need the sum of the length and the width ($l + w$).
Step 3: Detailed Explanation:
Analyze Statement (1): "The perimeter of the square is 24 inches."
This statement provides information about a square. However, the initial problem statement does not establish any relationship between this square and the triangle or the rectangle. Knowing the square's perimeter (and thus its side length and area) does not give us any information about the dimensions of the rectangle. Therefore, Statement (1) alone is not sufficient.
Analyze Statement (2): "The sum of the length and the width is 13 inches."
This statement directly gives us the value of \( (l + w) \).
\[ l + w = 13 \text{ inches} \] Using the perimeter formula:
\[ P = 2(l + w) = 2(13) = 26 \text{ inches} \] This statement allows us to calculate a unique value for the perimeter of the rectangle. Therefore, Statement (2) alone is sufficient.
Step 4: Final Answer:
Since Statement (2) alone is sufficient and Statement (1) alone is not sufficient, the correct option is (B). The information about the triangle and its area being equal to the rectangle's area is extra information not needed when considering Statement (2).