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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