Points P and Q are on the sides AB and BC respectively of a triangle ABC, right angled at B. If AQ = 11 cm, PC = 8 cm, and AC = 13 cm, then find the length (in cm) of PQ.

4

In any right angled triangle like above

a = √(\( {b }^{2 } \) + \( {c }^{2 } \) - \( {d }^{2 } \))

In the question, we have b = 11, c = 8 and d = 13

So, a = √(\( {11 }^{2 } \) + \( {8 }^{2 } \) - \( {13 }^{2 } \))

= a = \(\sqrt {16 }\) = 4 cm

Therefore, PQ = 4 cm.