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## OGQR 2020: Question No. 220

If A is the area of a triangle with sides of lengths x, y, and z as shown above, what is the value of A?

1. z = 13
2. A = 5y/2
 Source OGQR 2020 Type Data Sufficiency Topic Geometry Sub-Topic Triangles Difficulty Medium

### Solution

#### Steps 1 & 2: Understand Question and Draw Inferences

In this question, we are given:

• A right-angle triangle of area A
• Side lengths of the triangle are: x, y, and z.

We need to find:

• The value of A.

Now, the given triangle is a right-angled triangle.

• Hence, its area A = 1/2 * xy

Therefore, if we know the value of x and y or their product, we can find the value of A.

With this understanding, let us now analyse the individual statements.

#### Step 3: Analyse Statement 1

“z = 13”

Since we do not get the values of x and y from this statement, statement 1 is not sufficient to answer the question.

#### Step 4: Analyse Statement 2

“A = 5y/2

• 1/2 * xy = 5y/2

Or, x = 5

However, we do not know the value of y.

Therefore, statement 2 is not sufficient to answer the question.

#### Step 5: Combine Both Statements Together (If Needed)

From statement 1: z =13

From statement 2: x = 5

On applying Pythagoras theorem in the given triangle, we get: x2 + y2 = z2

• 52 + y2 = 132

From this equation, we can find y.

• Hence, we can find the value of A.

Since we could find the answer by combining both the statements, option C is the correct answer.