Mathematics
In the given figure, AB = 16 cm, BC = 12 cm and CA = 6 cm; find the length of CD.
Pythagoras Theorem
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Answer
By formula,
By pythagoras theorem,
⇒ (Hypotenuse)2 = (Perpendicular)2 + Base2
Let CD be x cm.
In right angle triangle ACD,
By pythagoras theorem,
⇒ AC2 = AD2 + CD2
⇒ 62 = AD2 + x2
⇒ 36 = AD2 + x2
⇒ AD2 = 36 - x2 ……..(1)
In right angle triangle ABD,
By pythagoras theorem,
⇒ AB2 = AD2 + BD2
⇒ 162 = AD2 + (BC + CD)2
⇒ 256 = 36 - x2 + (12 + x)2 [From equation (1)]
⇒ 256 = 36 - x2 + 122 + x2 + 2(12)x
⇒ 256 = 36 + 144 + 24x
⇒ 256 = 180 + 24x
⇒ 24x = 256 - 180
⇒ 24x = 76
⇒ x = cm.
Hence, CD = cm.
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