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CAT 2003 Slot 1 — QA Question 25

Similarity of TrianglesEasy
Passage / Data

Each question is followed by two statements, A and B. Answer each question using the following instructions

Choose 1 if the question can be answered by using one of the statements alone but not by using the other statement alone.
Choose 2 if the question can be answered by using either of the statements alone.
Choose 3 if the question can be answered by using both statements together but not by either statement alone.
Choose 4 if the question cannot be answered on the basis of the two statements.

D, E, F are the mid-points of the sides AB, BC and CA of triangle ABC respectively. What is the area of DEF in square centimetres?

A. AD = 1 cm, DF = 1 cm and perimeter of DEF = 3 cm
B. Perimeter of ABC = 6 cm, AB = 2 cm, and AC = 2 cm

Answer & solution

  • A

    1

  • 2

  • C

    3

  • D

    4

Solution

D, E and F are the midpoints of AB, BC and CA respectively.

Using statement A alone:

∵ AD = 1 cm

∴ BD = 1 cm                       …(Since D is the mid-point)

∵ DF = 1 cm

∴ BC = 2 cm                       …(Since D and F are the mid-points and DF is  parallel to BC)

∴ BE = 1 cm and EC = 1 cm

∵ Perimeter of DEF = 3 cm

∴ EF = 1 cm

∴ Area of ∆DEF can be obtained.

So, statement A alone is sufficient to obtain the answer.

Using statement B alone:

∵ Perimeter of ∆ABC = 6 cm, AB = 2 cm, AC = 2 cm

∴ BC = 2 cm

∴ DE = 1, EF = 1 and DF = 1

​​​​​​​​​​​​​​

So, statement B alone is also sufficient to obtain the answer.

Hence, option (b).

CAT 2003 Slot 1 QA Q25: D, E, F are the mid-points of the sides AB, BC and CA of triangle ABC respectively. What is the area of DEF in — Solution | TheCATExam