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Solution

Steps 1 & 2: Understand Question and Draw Inferences

In this question, we are given

• In a right triangle, x and y are the lengths of the legs.

We need to determine

• The value of xy.

Since we have no other relevant information about x and y present in the question stem, let us now analyse the individual statements.

 

Step 3: Analyse Statement 1

As per the information given in statement 1, the hypotenuse of the triangle is 10√2.

Applying Pythagoras Theorem, we can say

• x² + y² = (10√2)²

From this equation, we cannot determine the unique value of x and y, and hence, cannot determine the value of xy.

Hence, statement 1 is not sufficient to answer the question.

 

Step 4: Analyse Statement 2

As per the information given in statement 2, the area of the triangular region is 50.

Using the area of the right-angled triangle, we can say

• (1/2) xy = 50

Or, xy = 100

As we can determine the value of xy, statement 2 is sufficient to answer the question.

 

Step 5: Combine Both Statements Together (If Needed)

Since we can determine the answer from statement 2 individually, this step is not required.

Hence, the correct answer choice is option B.