How do you solve this trigonometry question?

Question

if the hypotenuse of the original right triangle is 100cm, and a vertical line splits the base of the triangle into 2 parts, one with a length of 64cm and the other of 36cm, what are the side lengths of the original right angled triangle?

Answer 1

Let the legs be a and b,

then a² = 36(100) ⇒ a = 60 cm

       b² = 64(100) ⇒ b = 80 cm

 

This is the result of the geometric mean theorem in a right triangle.