Mathematics

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

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 = $\dfrac{76}{24} = 3\dfrac{1}{6}$ cm.

Hence, CD = $3\dfrac{1}{6}$ cm.

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