Answer:
The shorter leg, s, is the geometric mean between h and m
The longer leg, b, is the geometric mean between h and n
Step-by-step explanation:
By the right triangle geometric mean theorem, we have;
The altitude of a right triangle, 'h', which intersects with the hypotenuse side of the right triangle at a point such that it creates two segments, 'a' and 'b' on the hypotenuse side , then we have;
h = √(a·b)
Therefore, we have;
Description [tex]{}[/tex] Proportion
The altitude of ΔAYES is the geometric mean between m and n [tex]\dfrac{m}{a} =\dfrac{a}{n}[/tex]
a² = m·n → a = √(m·n)
The shorter leg, s, is the geometric mean between h and m [tex]\dfrac{m}{s} =\dfrac{s}{h}[/tex]
s² = m·h → s = √(m·h)
The longer leg, b, is the geometric mean between h and n [tex]\dfrac{n}{b} =\dfrac{b}{h}[/tex]
b² = n·h → s = √(n·h)
