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Mathematics

In the given figure, BC = 16 cm, BD = 4 cm, then AB is equal to :

  1. 5 cm

  2. 8 cm

  3. 6 cm

  4. 4 cm

In the given figure, BC = 16 cm, BD = 4 cm, then AB is equal to : Model Question Paper - 2, Concise Mathematics Solutions ICSE Class 10.

Pythagoras Theorem

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Answer

From figure,

CD = BC - BD = 16 - 4 = 12 cm.

In right-angled triangle ABD,

By pythagoras theorem,

⇒ AB2 = AD2 + BD2

⇒ AB2 = AD2 + 42

⇒ AD2 = AB2 - 42 ………(1)

In right-angled triangle ABC,

⇒ BC2 = AC2 + AB2

⇒ AC2 = BC2 - AB2 ……….(2)

In right-angled triangle ADC,

⇒ AC2 = AD2 + CD2

⇒ AC2 = AD2 + 122

From equation (2),

⇒ BC2 - AB2 = AD2 + 122

⇒ 162 - AB2 = AD2 + 122

⇒ AD2 = 162 - AB2 - 122 ……….(3)

From equation (1) and (3), we get :

⇒ AB2 - 42 = 162 - AB2 - 122

⇒ AB2 + AB2 = 162 + 42 - 122

⇒ 2AB2 = 256 + 16 - 144

⇒ 2AB2 = 128

⇒ AB2 = 1282\dfrac{128}{2}

⇒ AB2 = 64

⇒ AB = 64\sqrt{64} = 8 cm.

Hence, Option 2 is the correct option.

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