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##