Mathematics

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

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In right angle △DBC,

By pythagoras theorem,

⇒ DB² = DC² + BC²

⇒ DB² = 12² + 3²

⇒ DB² = 144 + 9

⇒ DB² = 153.

⇒ DB = $\sqrt{153}$ .

In right angle △ABD,

By pythagoras theorem,

⇒ AD² = AB² + DB²

⇒ 13² = AB² + 153

⇒ 169 - 153 = AB²

⇒ AB² = 16

⇒ AB = $\sqrt{16}$ = 4 cm.

Hence, AB = 4 cm.

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