In the given figure, ABCD is a quadrilateral in which BC = 3 cm, AD = 13 cm, DC = 12 cm and ∠ABD = ∠BCD = 90°. Calculate the length of AB.
Pythagoras Theorem
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Question

In the given figure, ABCD is a quadrilateral in which BC = 3 cm, AD = 13 cm, DC = 12 cm and ∠ABD = ∠BCD = 90°. Calculate the length of AB.

KnowledgeBoat · Accepted Answer

In right angled triangle BCD,

By Pythagoras theorem,

Hypotenuse² = Perpendicular² + Base²

In triangle BCD,

⇒ BD² = CD² + BC²

⇒ BD² = 12² + 3²

⇒ BD² = 144 + 9

⇒ BD² = 153

⇒ BD = $\sqrt{153}$ cm.

In triangle ABD,

⇒ AD² = AB² + BD²

⇒ 13² = AB² + ( $\sqrt{153}$ )²

⇒ 169 = AB² + 153

⇒ AB² = 169 - 153

⇒ AB² = 16

⇒ AB = $\sqrt{16}$

⇒ AB = 4 cm.

Hence, length of AB = 4 cm.

Mathematics