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In figure given below, ∠D = 90°, AB = 16 cm, BC = 12 cm and CA = 6 cm. Find CD.

In figure, ∠D = 90°, AB = 16 cm, BC = 12 cm and CA = 6 cm. Find CD. Pythagoras Theorem, ML Aggarwal Understanding Mathematics Solutions ICSE Class 9.

Pythagoras Theorem

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Answer

Let CD be x cm.

In right angle △ACD,

By pythagoras theorem,

⇒ AC2 = AD2 + CD2

⇒ 62 = AD2 + x2

⇒ AD2 = 36 - x2 …….(i)

In right angle △ABD,

By pythagoras theorem,

⇒ AB2 = AD2 + BD2

⇒ 162 = (36 - x2) + (12 + x)2

⇒ 256 = 36 - x2 + 144 + x2 + 24x

⇒ 256 = 180 + 24x

⇒ 24x = 76

⇒ x = 7624=316\dfrac{76}{24} = 3\dfrac{1}{6} cm.

Hence, CD = 3163\dfrac{1}{6} cm.

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