If in an isosceles right triangle ABC the two sides AC BC

If in an isosceles right triangle ABC, the two sides |AC| = |BC| = 4 cm, calculate the length of perpendicular from vertex C to side AB.

Solution

|AC | = | BC | = 4cm

isoceles right triangle has one angle 90 and other 2 angles are 45 and 45

length of hypotenuse is sqrt 2 a

a = 4

hypotenuse = 4 sqrt 2

the perpendicular will bisect AB

therefore , length of perpendicular is 4sqrt 2 / 2 = 2 sqrt 2