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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


Team Careers360 1st Jan, 2024
Answer (1)
Team Careers360 22nd Jan, 2024

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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