CAT Exam Model Paper 5 with solutions for free online practice

Question : 7 of 60

Marks: +1, -0

In the given figure ABCD is a quadrilateral with BC = 4 cm and AD = 2 cm.

What is the length of AB (in cm)?

Solution:

∠BAD = 90°

Extend BA and CD to meet at E.
ΔEBC becomes an equilateral triangle.
So BE = 4 cm
InΔADE, ∠ADE = 30°

\tan 30° = { A E } /{ 2 } = { 1 } /{√ { 3 } }

⇒ \A \E = { 2 } /{ √ { 3 } } { \cm }

∴A B = B E - A E = 4 - { 2 } { √ { 3 } }

= { 4 √ { 3 } - 2 } /{ √ { 3 } } { \cm }

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