h = 2.4, m=1.8, n=3.2
1) Since this is a right triangle we can write it out the following relationships based on the similarity of triangles:
ah =bc a= hypotenuse, b and c legs and h the height. Plug into that:
xh=3*4
5h=3*4
h=12/5 h = 2.4
b²=a*m the square of b² is the product of a and its projection
3²=5*m
3² = 5m
m= 9/5
m= 1.8
c² = a.n C² is the product of the hypotenuse by its projection
4²=5*n
4²=5n
n=16/5
n= 3.2
2) Hence, the answer is m=1.8, n=3.2, h=2.4