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## OGQR 2020: Question No.206

In the figure above, is the area of the triangular region ADE equal to the area of rectangular region ABCD?

1. x = 10 and y = 5.
2. x = 2y

### Solution

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

We are given a quadrilateral ABCD that includes

• Length of DE = x and DC = y

We need to determine:

• Whether the area of ∆ADE = area of rectangle ABCD or not.
• Or, 1/2 * AD * DE = AB * BC
• Or, 1/2 * AD * DE = CD * AD (Since ABCD is a rectangle, AB = CD = y and AD = BC)
• Or, 1/2 * x = y (Since AD is side length, it cannot be negative. Hence, we can divide both the sides of the inequality by AD)
• Or, x = 2y
• Therefore, if x = 2y then the answer is Yes, else the answer is No.

With this understanding let us analyze the statements.

#### Step 3: Analyse Statement 1

“x = 10 and y = 5”

• 10 = 2 * 5

Since x = 2y, the answer to the question is Yes.

Thus, statement 1 is sufficient to answer the question.

#### Step 4: Analyse Statement 2

“x = 2y”

Since x = 2y, the answer to the question is Yes.

Thus, statement 2 is sufficient to answer the question.

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

Since we could determine the answer from either of the statements individually, this step is not required.

Hence, the correct answer is option D.

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