Question : Let ABC and PQR be two congruent triangles such that $\angle A = \angle P = 90^{\circ}$. If BC = 17 cm, PR = 8 cm, find AB (in cm).
Option 1: 12
Option 2: 15
Option 3: 14
Option 4: 9
Correct Answer: 15
Solution : $\angle A = \angle P = 90^{\circ}$ BC = 17 cm PR = 8 cm Since $\triangle ABC$ is congruent to $\triangle PQR$, AC = PR = 8 cm By Pythagoras theorem, $BC^2 = AB^2 + AC^2$ ⇒ $17^2 = AB^2 + 8^2$ ⇒ $289 = AB^2 + 64$ ⇒ $AB^2 = 289 - 64 = 225$ ⇒ $AB = 15$ Hence, the correct answer is 15.
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