Let ΔABC and ΔPQR be two congruent right-angled triangles such that A = P = 90°. If BC = 13 cm and PR = 12 cm, then find the length of AB.
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 5 cm.
△ABC ≅ △PQR
Two triangles are congruent if their corresponding sides are equal in length and their corresponding angles are equal in measure.
AC = PR = 12 cm and BC = QR = 13 cm
In ΔPQR, PQ2 + PR2 = QR2
⇒ PQ2 + 122 = 132
⇒ PQ2 + 144 = 169
⇒ PQ2 = 169 - 144 = 25
⇒ PQ = √25 = 5 cm
⇒ AB = 5 cm
Hence, the length of AB is 5 cm.