Question : Let ABC and PQR be two congruent triangles such that $\angle $A = $\angle $P = $90^{\circ}$. If BC = 13 cm, PR = 5 cm, find AB.
Option 1: 12 cm
Option 2: 8 cm
Option 3: 10 cm
Option 4: 5 cm
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Correct Answer: 12 cm
Solution : Given: $\triangle ABC$ and $\triangle PQR$ $\angle $A = $\angle $P = $90^{\circ}$ BC = 13 cm and PR = 5 cm $\because$ Both the triangles are congruent BC = QR and AC = PR By using Pythagoras' theorem: h 2 = p 2 + b 2 Where h is the hypotenuse, p is the perpendicular, and b is the base. BC 2 = AC 2 + AB 2 ⇒13 2 = 5 2 + AB 2 ⇒ 169 – 25 = AB 2 ⇒ AB = 12 Hence, the correct answer is 12 cm.
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