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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