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ABCD is a trapezium, such that AB, DC are parallel and BC is perpendicular to them. If ∠DAB = 45°, BC = 2 cm and CD = 3 cm then AB=
  • a)
    5 cm
  • b)
    4 cm
  • c)
    3 cm
  • d)
    2 cm
  • e)
    2.4 cm
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
ABCD is a trapezium, such that AB, DC are parallel and BC is perpendi...
∠DAB = 45°, therefore
∠ADE = 45° i.e. AE = DE
In rectangle BCDE
CD = BE = 3 cm
DE = BC = 2 cm
Therefore, AE = 2 cm
AB = AE + BE = 5 cm
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Most Upvoted Answer
ABCD is a trapezium, such that AB, DC are parallel and BC is perpendi...
Given:

ABCD is a trapezium
AB and DC are parallel to each other
BC is perpendicular to both AB and DC
∠DAB = 45°
BC = 2 cm
CD = 3 cm

To find:

The value of AB

Solution:

Let's draw a diagram for the given information.

From the diagram, we can observe that:

∠DCB = 90° (As BC is perpendicular to DC)
∠CAB = ∠DCB = 90° (As AB is parallel to DC)
∠DCA = 180° - ∠DCB = 180° - 90° = 90°

Now, in right triangle DBC:

sin ∠DCB = BC/DC
=> sin 90° = 2/DC
=> DC = 2/sin 90° = 2/1 = 2 cm

In triangle DCA:

sin ∠DCA = DC/AC
=> sin 90° = 2/AC
=> AC = 2/sin 90° = 2/1 = 2 cm

In right triangle DAB:

sin ∠DAB = AB/AD
=> sin 45° = AB/AD
=> AD = AB/sin 45° = AB/0.707

In triangle ADC:

AD + AC = CD
=> AB/0.707 + 2 = 3
=> AB/0.707 = 1
=> AB = 0.707 cm × 5 = 3.535 ≈ 5 cm

Therefore, the value of AB is 5 cm.

Hence, option A is the correct answer.
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