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If x and y are the lengths of the legs of a right triangle, what is the value of xy? – OG 2020 Question #334 with Solution

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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?

  1. The hypotenuse of the triangle is 10āˆš2.
  2. 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 10āˆš2.

Applying Pythagoras Theorem, we can say

  • x2 + y2 = (10āˆš2)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.

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