OG 2020: Question No. 334
If x and y are the lengths of the legs of a right triangle, what is the value of xy?
- The hypotenuse of the triangle is 10ā2.
- The area of the triangular region is 50.
Source | OG 2020 |
Type | Data Sufficiency |
Topic | Geometry |
Sub-Topic | Triangles |
Difficulty | Easy – Medium |
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 10ā2.
Applying Pythagoras Theorem, we can say
- x2 + y2 = (10ā2)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.