A 45-45-90 triangle has a hypotenuse of length 7. What is the length of one of its legs?

##(7√2)/2##

∵ It is a 45-45-90 triangle, ∴ It is a isosceles Rt △ ∴ two catheti are equal to each other. ∵ Pythagoras’ theorem ∴ cathetus² + cathetus² = hypotenuse² ∴ 2 × cathetus² = hypotenuse² ∵ hypotenuse = 7 ∴ 2 × cathetus² = 7² ∴ 2 × cathetus² = 49 ∴ cathetus² = ##49/2## ∵ cathetus＞0 ∴ cathetus = ##√49/2## ∴ cathetus = ##(7√2)/2## ∴ The length of one of its any legs is ##(7√2)/2##