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In the figure above, is the area of triangular region ADE equal to the area of rectangular region ABCD? – OGQR 2020 Question #206 with Solution

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
Source OGQR 2020
Type Data Sufficiency
Topic Geometry
Sub-Topic Triangle/Polygons
Difficulty Medium

Solution

Steps 1 & 2: Understand Question and Draw Inferences

We are given a quadrilateral ABCD that includes

  • ∆ADE and Rectangle ABCD
  • 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 * AD * x = y * AD
    • 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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