Question

In the right-angled ∆LMN, ∠M = 90°. If l(LM) = 12 cm and l(LN) = 20 cm, find the length of seg MN.

Answer 1

In ∆LMN, ∠M = 90°. 

Hence, side LN is the hypotenuse. 

According to Pythagoras’ theorem, 

l(LN)² = l(LM)² + l(MN)² 

∴ 20² = 12² + l(MN)² 

∴ l(MN)² = 20² – 12²  

∴ l(MN)² = 400 – 144 

∴ l(MN)² = 256 

∴ l(MN)² = 16² 

∴ l(MN)= 16 cm 

∴ The length of seg MN is 16 cm.