## 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?

- z = 13
- 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__

__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__

__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__

__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)__

__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: x^{2} + y^{2} = z^{2}

- 5
^{2}+ y^{2}= 13^{2}

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.