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

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 =
⇒ AB2 = 64
⇒ AB = = 8 cm.
Hence, Option 2 is the correct option.
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