Directions: Each of the questions given below consists of a sta tement and/or a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statement(s) is/are sufficient to answer the question. Read both the statements and Give answer (a) if the data in Statement I alone are sufficient to answer the question, while the data in Statement II alone are not sufficient to answer the question; Give answer (b) if the data in Statement II alone are sufficient to answer the question, while the data in Statement I alone are not sufficient to answer the question; Give answer (c) if the data either in Statement I or in Statement II alone are sufficient to answer the question; Give answer (d) if the data even in both Statements I and II together are not sufficient to answer the question; Give answer (e) if the data in both Statements I and II together are necessary to answer the question. The area of a rectangle is equal to the area of a right-angled triangle. What is the length of the rectangle? I. The base of the triangle is 40 cm. II. The height of the triangle is 50 cm.

### Concept & Missing Variables We are establishing an equality between the area of a rectangle and the area of a right-angled triangle. $$ L \times B = \frac{1}{2} \times \text{base} \times \text{height} $$ ### Step-by-Step Solution 1. We are tasked with finding the length of the rectangle ($L$). To solve the equation for $L$, we need the base of the triangle, the height of the triangle, and the breadth ($B$) of the rectangle. 2. **Analyze Statement I:** Only the base of the triangle is given ($40 \text{ cm}$). We lack the height and the rectangle's breadth. Statement I is insufficient. 3. **Analyze Statement II:** Only the height of the triangle is given ($50 \text{ cm}$). We lack the base and the rectangle's breadth. Statement II is insufficient. 4. **Combine Statements I and II:** Together, we have the base ($40 \text{ cm}$) and height ($50 \text{ cm}$) of the triangle. We can calculate the triangle's area ($\frac{1}{2} \times 40 \times 50 = 1000 \text{ sq. cm}$). 5. Consequently, the rectangle's area ($L \times B$) is $1000 \text{ sq. cm}$. However, we still do not know the breadth ($B$) of the rectangle. Without $B$, $L$ could be any value (e.g., $10$ if $B=100$, or $25$ if $B=40$). The data remains insufficient. ### Exam Strategy & Shortcut Count the fundamental unknowns. The formula involves 4 variables: $L$, $B$, base, and height. The statements only provide values for 2 variables (base and height). Even when combined, 1 variable ($B$) remains completely unaccounted for, making it impossible to solve for the target variable ($L$). ### Common Pitfall A common trap is successfully calculating the area of the triangle and assuming that finding an area means the question is solved, completely forgetting that the rectangle still has two independent dimensions. ### Final Answer Therefore, the correct answer is **if the data even in both Statements I and II together are not sufficient to answer the question;**.