Triangles Test

Result

Triangles Test - 17

Score
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Rank
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Weekly Quiz Competition

Question 1
1 / -0

Use the following information to answer the next question.

In the given figure, BE||FC and DE||AF.

If BC = 2 cm and AD = 8 cm, then what is the perimeter of hexagon AFCDEBA?

A
38 cm

B
40 cm

C
42 cm

D
44 cm

Solution

In ΔDBE and ΔACF:

∠DBE = ∠ACF (Alternate interior angles)

∠EDB = ∠FAC (Alternate interior angles)

BE = CF = 9 cm

∴ ΔDBE ≅ ΔACF (ASA Congruence rule)

⇒ ED = FA and DB = AC (CPCT)

∴ ED = 7 cm

Now, DB = AC

∴ DC + CB = AB + BC

⇒ DC = AB … (1)

It is given that AD = 8 cm.

∴ AB + BC + CD = 8 cm

⇒ DC + 2 cm + CD = 8 cm

⇒ 2CD = 6 cm

⇒ CD = 3 cm

∴ AB = 3 cm

Perimeter of hexagon AFCDEBA = AF + FC + CD + DE + EB + BA

= (7 + 9 + 3 + 7 + 9 + 3) cm

= 38 cm

Thus, the perimeter of hexagon AFCDEBA is 38 cm.

The correct answer is A.