Chapter: Pythagoras Theorem· Mathematics Part 2 (Geometry)
Answer: LM = MN = 6 cm
\(\angle L = 180^\circ - 90^\circ - 45^\circ = 45^\circ\), so \(\Delta LMN\) is a 45°–45°–90° triangle and LM = MN.
By the 45°–45°–90° theorem, each side containing the right angle \(= \dfrac{1}{\sqrt{2}} \times \text{hypotenuse} = \dfrac{1}{\sqrt{2}} \times 6\sqrt{2} = 6\) cm.