किसी आयताकार खेत की लंबाई, चौड़ाई की तीन गुनी है यदि तो क्षेत्रफल कितना होगा ?

The question states that the length of a rectangular field is three times its width, but it is incomplete as it does not provide any specific value (like perimeter or one of the dimensions) to calculate the area. However, we can analyze the given options based on the relationship between length and width, and a common assumption in such problems that dimensions are integers.

Step 1: Define variables and set up the relationship. Let the width of the rectangular field be $w$ meters. The length $l$ is three times the width: $l = 3w$

Step 2: Express the area in terms of $w$. The area $A$ of a rectangle is given by the formula $A = l \times w$. Substitute $l = 3w$ into the area formula: $A = (3w) \times w = 3w^2$ This means the area must be a multiple of 3.

Step 3: Evaluate the options based on the area formula and the assumption of integer dimensions. We will check which option for the area $A$ allows for integer values for the width $w$ (and consequently, the length $l$).

• A. 64 वर्ग मीटर: $64 \div 3$ is not an integer. Therefore, $64$ cannot be $3w^2$.
• B. 48 वर्ग मीटर: If $A = 48$, then $3w^2 = 48$. $w^2 = \frac{48}{3} = 16$ $w = \sqrt{16} = 4 \text{ meters}$ If $w = 4$ meters, then $l = 3 \times 4 = 12$ meters. Both dimensions are integers.
• C. 54 वर्ग मीटर: If $A = 54$, then $3w^2 = 54$. $w^2 = \frac{54}{3} = 18$ $w = \sqrt{18} = 3\sqrt{2} \text{ meters}$ The width is not an integer.
• D. 42 वर्ग मीटर: If $A = 42$, then $3w^2 = 42$. $w^2 = \frac{42}{3} = 14$ $w = \sqrt{14} \text{ meters}$ The width is not an integer.

Step 4: Select the correct option. Given that option B (48 वर्ग मीटर) is the only one that results in integer dimensions for the length and width, it is the most plausible answer, assuming the problem intends for integer dimensions.

The final answer is $\boxed{B. 48 वर्ग मीटर}$.